3.3 Övningar
Sommarmatte 1
(Skillnad mellan versioner)
| Versionen från 29 april 2007 kl. 13.15 (redigera) Ossiang (Diskussion | bidrag) (→Övning 3.3:6) ← Gå till föregående ändring |
Nuvarande version (31 maj 2007 kl. 07.02) (redigera) (ogör) KTH.SE:u1rp004j (Diskussion | bidrag) |
||
| (8 mellanliggande versioner visas inte.) | |||
| Rad 1: | Rad 1: | ||
| + | |||
| ==Övning 3.3:1== | ==Övning 3.3:1== | ||
| <div class="ovning"> | <div class="ovning"> | ||
| - | Bestäm x om | + | Bestäm $\,x\,$ om |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">10^x=1\,000</td> | + | <td class="ntext" width="50%">10^x=1\,000</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">10^x=0,1</td> | + | <td class="ntext" width="50%">$10^x=0{,}1$</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">\displaystyle \frac{1}{10^x}=100</td> | + | <td class="ntext" width="50%">\displaystyle \frac{1}{10^x}=100</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">\displaystyle \frac{1}{10^x}=0,000\,1</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{10^x}=0{,}000\,1$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 21: | Rad 23: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">x=3</td> | + | <td class="ntext" width="50%">x=3</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">x=-1</td> | + | <td class="ntext" width="50%">x=-1</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">x=-2</td> | + | <td class="ntext" width="50%">x=-2</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">x=4</td> | + | <td class="ntext" width="50%">x=4</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 40: | Rad 43: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_3_1a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_1a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 48: | Rad 58: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_3_1b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_1b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 56: | Rad 73: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_3_1c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_1c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 64: | Rad 88: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_3_1d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_1d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 75: | Rad 106: | ||
| Beräkna | Beräkna | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">\lg{ 0,1}</td> | + | <td class="ntext" width="25%">$\lg{ 0{,}1}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">\lg{ 10\,000}</td> | + | <td class="ntext" width="25%">\lg{ 10\,000}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">\lg {0,001}</td> | + | <td class="ntext" width="25%">$\lg {0{,}001}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">\lg {1}</td> | + | <td class="ntext" width="25%">\lg {1}</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">10^{\lg{2}}</td> | + | <td class="ntext" width="25%">10^{\lg{2}}</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">\lg{10^3}</td> | + | <td class="ntext" width="25%">\lg{10^3}</td> |
| <td class="ntext">g)</td> | <td class="ntext">g)</td> | ||
| - | <td class="ntext">10^{-\lg{0,1}}</td> | + | <td class="ntext" width="25%">$10^{-\lg{0{,}1}}$</td> |
| <td class="ntext">h)</td> | <td class="ntext">h)</td> | ||
| - | <td class="ntext">\lg{\displaystyle \frac{1}{10^2}}</td> | + | <td class="ntext" width="25%">\lg{\displaystyle \frac{1}{10^2}}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| </table> | </table> | ||
| - | |||
| </div> | </div> | ||
| Rad 105: | Rad 133: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">-1</td> | + | <td class="ntext" width="25%">-1</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">4</td> | + | <td class="ntext" width="25%">4</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">-3</td> | + | <td class="ntext" width="25%">-3</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">0</td> | + | <td class="ntext" width="25%">0</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">2</td> | + | <td class="ntext" width="25%">2</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">3</td> | + | <td class="ntext" width="25%">3</td> |
| <td class="ntext">g)</td> | <td class="ntext">g)</td> | ||
| - | <td class="ntext">10</td> | + | <td class="ntext" width="25%">10</td> |
| <td class="ntext">h)</td> | <td class="ntext">h)</td> | ||
| - | <td class="ntext">-2</td> | + | <td class="ntext" width="25%">-2</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 135: | Rad 161: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_3_2a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_3_2b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_3_2c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_3_2d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:3_3_2e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning f </div> | + | <div class=NavHead>Lösning f) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga f<br \>[[Bild:3_3_2f.gif]] | + | Lösning till delfråga f) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning g </div> | + | <div class=NavHead>Lösning g) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga g<br \>[[Bild:3_3_2g.gif]] | + | Lösning till delfråga g) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2g.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning h </div> | + | <div class=NavHead>Lösning h) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga h<br \>[[Bild:3_3_2h.gif]] | + | Lösning till delfråga h) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_2h.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 202: | Rad 277: | ||
| Beräkna | Beräkna | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">\log_2{8}</td> | + | <td class="ntext" width="33%">\log_2{8}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">\log_9{\displaystyle \frac{1}{3}}</td> | + | <td class="ntext" width="33%">\log_9{\displaystyle \frac{1}{3}}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">\log_2{0,125}</td> | + | <td class="ntext" width="33%">$\log_2{0{,}125}$</td> |
| - | <td class="ntext">d)</td> | + | |
| - | <td class="ntext">$\log_3{\left(9\cdot3^{1/3}\right)}$</td> | + | |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">\log_3{\left(9\cdot3^{1/3}\right)}</td> | ||
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">2^{\log_{\scriptstyle2}{4}}</td> | + | <td class="ntext" width="33%">2^{\log_{\scriptstyle2}{4}}</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">\log_2{4}+\log_2{\displaystyle \frac{1}{16}}</td> | + | <td class="ntext" width="33%">\log_2{4}+\log_2{\displaystyle \frac{1}{16}}</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">g)</td> | <td class="ntext">g)</td> | ||
| - | <td class="ntext">\log_3{12}-\log_3{4}</td> | + | <td class="ntext" width="33%">\log_3{12}-\log_3{4}</td> |
| <td class="ntext">h)</td> | <td class="ntext">h)</td> | ||
| - | <td class="ntext">$\log_a{\left(a^2\sqrt{a}\right)}$</td> | + | <td class="ntext" width="33%">$\log_a{\bigl(a^2\sqrt{a}\,\bigr)}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 231: | Rad 306: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">3</td> | + | <td class="ntext" width="33%">3</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">-\displaystyle \frac{1}{2}</td> | + | <td class="ntext" width="33%">-\displaystyle \frac{1}{2}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">-3</td> | + | <td class="ntext" width="33%">$-3$</td> |
| - | <td class="ntext">d)</td> | + | |
| - | <td class="ntext">$\displaystyle \frac{7}{3}$</td> | + | |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">\displaystyle \frac{7}{3}</td> | ||
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">4</td> | + | <td class="ntext" width="33%">4</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">-2</td> | + | <td class="ntext" width="33%">-2</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">g)</td> | <td class="ntext">g)</td> | ||
| - | <td class="ntext">1</td> | + | <td class="ntext" width="33%">1</td> |
| <td class="ntext">h)</td> | <td class="ntext">h)</td> | ||
| - | <td class="ntext">\displaystyle \frac{5}{2}</td> | + | <td class="ntext" width="33%">\displaystyle \frac{5}{2}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 261: | Rad 336: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_3_3a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_3_3b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_3_3c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_3_3d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:3_3_3e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning f </div> | + | <div class=NavHead>Lösning f) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga f<br \>[[Bild:3_3_3f.gif]] | + | Lösning till delfråga f) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning g </div> | + | <div class=NavHead>Lösning g) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga g<br \>[[Bild:3_3_3g.gif]] | + | Lösning till delfråga g) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3g.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | |||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning h </div> | + | <div class=NavHead>Lösning h) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga h<br \>[[Bild:3_3_3h.gif]] | + | Lösning till delfråga h) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_3h.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 328: | Rad 452: | ||
| Förenkla | Förenkla | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">\lg{50}-\lg{5}</td> | + | <td class="ntext" width="33%">\lg{50}-\lg{5}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">\lg{23}+\lg{\displaystyle \frac{1}{23}}</td> | + | <td class="ntext" width="33%">\lg{23}+\lg{\displaystyle \frac{1}{23}}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</td> | + | <td class="ntext" width="33%">\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 344: | Rad 467: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">1</td> | + | <td class="ntext" width="33%">1</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">0</td> | + | <td class="ntext" width="33%">0</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">-\displaystyle \frac{1}{2}\lg{3}</td> | + | <td class="ntext" width="33%">-\displaystyle \frac{1}{2}\lg{3}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 361: | Rad 483: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_3_4a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_4a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_3_4b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_4b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_3_4c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_4c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 386: | Rad 529: | ||
| Förenkla | Förenkla | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">\ln{e^3}+\ln{e^2}</td> | + | <td class="ntext" width="33%">\ln{e^3}+\ln{e^2}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">\ln{8}-\ln{4}-\ln{2}</td> | + | <td class="ntext" width="33%">\ln{8}-\ln{4}-\ln{2}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">(\ln{1})\cdot e^2</td> | + | <td class="ntext" width="33%">(\ln{1})\cdot e^2</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">\ln{e}-1</td> | + | <td class="ntext" width="33%">\ln{e}-1</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">\ln{\displaystyle \frac{1}{e^2}}</td> | + | <td class="ntext" width="33%">\ln{\displaystyle \frac{1}{e^2}}</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">\left(e^{\ln{e}}\right)^2</td> | + | <td class="ntext" width="33%">\left(e^{\ln{e}}\right)^2</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 411: | Rad 552: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">5</td> | + | <td class="ntext" width="33%">5</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">0</td> | + | <td class="ntext" width="33%">0</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">0</td> | + | <td class="ntext" width="33%">0</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">0</td> | + | <td class="ntext" width="33%">0</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">-2</td> | + | <td class="ntext" width="33%">-2</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">e^2</td> | + | <td class="ntext" width="33%">e^2</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 437: | Rad 576: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_3_5a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_5a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_3_5b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_5b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_3_5c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_5c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_3_5d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_5d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:3_3_5e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_5e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning f </div> | + | <div class=NavHead>Lösning f) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga f<br \>[[Bild:3_3_5f.gif]] | + | Lösning till delfråga f) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_5f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 480: | Rad 661: | ||
| ==Övning 3.3:6== | ==Övning 3.3:6== | ||
| - | <div class="ovning"><table width="100%" cellspacing="10px"> | + | <div class="ovning"> |
| - | <tr> | + | [[Bild:miniraknare.gif||right]] |
| - | <td> | + | Använd miniräknaren till höger för att beräkna med tre decimaler (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''): |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"><td height="5px"/></tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="100%">\log_3{4}</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="100%">\lg{46}</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="100%">\log_3{\log_2{(3^{118})}}</td> | ||
| + | </tr> | ||
| + | <tr align="left"><td height="40px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| - | Använd miniräknaren till höger för att beräkna med tre decimaler. (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''.) | + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> | ||
| + | <div class=NavContent> | ||
| + | Facit till alla delfrågor | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"><td height="5px"/></tr> | <tr align="left"><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">$\log_3{4}$</td> | + | <td class="ntext" width="100%">$1{,}262$</td> |
| </tr> | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\lg{46}$</td> | + | <td class="ntext" width="100%">$1{,}663$</td> |
| </tr> | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$\log_3{\log_2{(3^{118})}}$</td> | + | <td class="ntext" width="100%">$4{,}762$</td> |
| </tr> | </tr> | ||
| <tr align="left"><td height="5px"/></tr> | <tr align="left"><td height="5px"/></tr> | ||
| - | </table></td> | + | </table> |
| - | <td> | + | |
| - | <!-- Miniräknare --> | + | |
| - | <div> | + | |
| - | <form onsubmit="keyclick('='); return false;"> | + | |
| - | <div id="calculator" class="drag"> | + | |
| - | <div class="calculatorcontainer"> | + | |
| - | <input type="text" name="input" size="16" id="result" value="0" | + | |
| - | onclick="this.focus()" onkeyup="addToCalcDirect(this.value)"> | + | |
| - | <br/> | + | |
| - | <input type="button" value="AC" onclick="keyclick(this.value)"><input type="button" value="C" onclick="keyclick(this.value)"><input type="button" value="LN" onclick="keyclick(this.value)"><input type="button" value="×" onclick="keyclick(this.value)"><br/> | + | |
| - | <input type="button" value="7" onclick="keyclick(this.value)"><input type="button" value="8" onclick="keyclick(this.value)"><input type="button" value="9" onclick="keyclick(this.value)"><input type="button" value="÷" onclick="keyclick(this.value)"><br/> | + | |
| - | <input type="button" value="4" onclick="keyclick(this.value)"><input type="button" value="5" onclick="keyclick(this.value)"><input type="button" value="6" onclick="keyclick(this.value)"><input type="button" value="+" onclick="keyclick(this.value)"><br/> | + | |
| - | <input type="button" value="1" onclick="keyclick(this.value)"><input type="button" value="2" onclick="keyclick(this.value)"><input type="button" value="3" onclick="keyclick(this.value)"><input type="button" value="-" onclick="keyclick(this.value)"><br/> | + | |
| - | <input type="button" value="+/-" onclick="keyclick(this.value)"><input type="button" value="0" onclick="keyclick(this.value)"><input type="button" value="." onclick="keyclick(this.value)"><input type="button" value="=" onclick="keyclick(this.value)"> | + | |
| </div> | </div> | ||
| </div> | </div> | ||
| - | </form> | + | |
| - | </div> | + | <div class=NavFrame style="CLEAR: both"> |
| - | <!-- Slut miniräknare --> | + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> | ||
| + | Lösning till delfråga a) | ||
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_6a-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_6a-2(2).gif]] | ||
| </td> | </td> | ||
| </tr> | </tr> | ||
| </table> | </table> | ||
| + | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Facit </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Lösning till delfråga b) |
| - | + | <table width="100%"> | |
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_6b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga <br \>[[Bild:]] | + | Lösning till delfråga c) |
| + | <table width="100%"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_6c-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_3_6c-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
Nuvarande version
Innehåll[göm] |
[redigera] Övning 3.3:1
Bestäm \,x\, om
| a) | 10^x=1\,000 | b) | 10^x=0{,}1 |
| c) | \displaystyle \frac{1}{10^x}=100 | d) | \displaystyle \frac{1}{10^x}=0{,}000\,1 |
Facit
Facit till alla delfrågor
| a) | x=3 | b) | x=-1 |
| c) | x=-2 | d) | x=4 |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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[redigera] Övning 3.3:2
Beräkna
| a) | \lg{ 0{,}1} | b) | \lg{ 10\,000} | c) | \lg {0{,}001} | d) | \lg {1} |
| e) | 10^{\lg{2}} | f) | \lg{10^3} | g) | 10^{-\lg{0{,}1}} | h) | \lg{\displaystyle \frac{1}{10^2}} |
Facit
Facit till alla delfrågor
| a) | -1 | b) | 4 | c) | -3 | d) | 0 |
| e) | 2 | f) | 3 | g) | 10 | h) | -2 |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Lösning f)
Lösning till delfråga f)
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Lösning g)
Lösning till delfråga g)
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Lösning h)
Lösning till delfråga h)
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[redigera] Övning 3.3:3
Beräkna
| a) | \log_2{8} | b) | \log_9{\displaystyle \frac{1}{3}} | c) | \log_2{0{,}125} |
| d) | \log_3{\left(9\cdot3^{1/3}\right)} | e) | 2^{\log_{\scriptstyle2}{4}} | f) | \log_2{4}+\log_2{\displaystyle \frac{1}{16}} |
| g) | \log_3{12}-\log_3{4} | h) | \log_a{\bigl(a^2\sqrt{a}\,\bigr)} | ||
Facit
Facit till alla delfrågor
| a) | 3 | b) | -\displaystyle \frac{1}{2} | c) | -3 |
| d) | \displaystyle \frac{7}{3} | e) | 4 | f) | -2 |
| g) | 1 | h) | \displaystyle \frac{5}{2} | ||
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Lösning f)
Lösning till delfråga f)
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Lösning g)
Lösning till delfråga g)
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Lösning h)
Lösning till delfråga h)
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[redigera] Övning 3.3:4
Förenkla
| a) | \lg{50}-\lg{5} | b) | \lg{23}+\lg{\displaystyle \frac{1}{23}} | c) | \lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}} |
Facit
Facit till alla delfrågor
| a) | 1 | b) | 0 | c) | -\displaystyle \frac{1}{2}\lg{3} |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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[redigera] Övning 3.3:5
Förenkla
| a) | \ln{e^3}+\ln{e^2} | b) | \ln{8}-\ln{4}-\ln{2} | c) | (\ln{1})\cdot e^2 |
| d) | \ln{e}-1 | e) | \ln{\displaystyle \frac{1}{e^2}} | f) | \left(e^{\ln{e}}\right)^2 |
Facit
Facit till alla delfrågor
| a) | 5 | b) | 0 | c) | 0 |
| d) | 0 | e) | -2 | f) | e^2 |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Lösning f)
Lösning till delfråga f)
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[redigera] Övning 3.3:6
Använd miniräknaren till höger för att beräkna med tre decimaler (Knappen LN betecknar den naturliga logaritmen i basen e):
| a) | \log_3{4} |
| b) | \lg{46} |
| c) | \log_3{\log_2{(3^{118})}} |
Facit
Facit till alla delfrågor
| a) | 1{,}262 |
| b) | 1{,}663 |
| c) | 4{,}762 |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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