3.3 Övningar

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Rad 1: Rad 1:
 +__NOTOC__
==Övning 3.3:1== ==Övning 3.3:1==
<div class="ovning"> <div class="ovning">
-Best&auml;m x om+Best&auml;m $\,x\,$ 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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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:
Ber&auml;kna Ber&auml;kna
<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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</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>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</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>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</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>L&ouml;sning h&nbsp;</div>+<div class=NavHead>L&ouml;sning h)&nbsp;</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:
Ber&auml;kna Ber&auml;kna
<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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</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>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</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>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</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>L&ouml;sning h&nbsp;</div>+<div class=NavHead>L&ouml;sning h)&nbsp;</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:
F&ouml;renkla F&ouml;renkla
<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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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:
F&ouml;renkla F&ouml;renkla
<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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</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>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</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 481: Rad 662:
<div class="ovning"> <div class="ovning">
-Anv&auml;nd minir&auml;knaren till h&ouml;ger f&ouml;r att ber&auml;kna med tre decimaler. (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''.)+[[Bild:miniraknare.png||right]]
 +Anv&auml;nd minir&auml;knaren till h&ouml;ger f&ouml;r att ber&auml;kna med tre decimaler (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''):
<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">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\log_3{4}$</td>+<td class="ntext" width="100%">$\log_3{4}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\lg{46}$</td>+<td class="ntext" width="100%">$\lg{46}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\log_3{\log_2{(3^{118})}}$</td>+<td class="ntext" width="100%">$\log_3{\log_2{(3^{118})}}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$\sqrt7$</td>+<td class="ntext" width="100%">$\sqrt7$</td>
</tr> </tr>
<tr align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
Rad 507: Rad 689:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</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 align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$1,262$</td>+<td class="ntext" width="100%">$1{,}262$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$1,663$</td>+<td class="ntext" width="100%">$1{,}663$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$4,762$</td>+<td class="ntext" width="100%">$4{,}762$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$2,646$</td>+<td class="ntext" width="100%">$2{,}646$</td>
</tr> </tr>
<tr align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
</table> </table>
- 
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:3_3_6a-1(2).gif]]<br \>[[Bild:3_3_6a-2(2).gif]]+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>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:3_3_6b.gif]]+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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:3_3_6c-1(2).gif]]<br \>[[Bild:3_3_6c-2(2).gif]]+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>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning &nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga <br \>[[Bild:3_3_6d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_6d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>

Versionen från 14 maj 2007 kl. 12.19

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) $\displaystyle \frac{1}{10^x}=0{,}000\,1$




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) $\lg{\displaystyle \frac{1}{10^2}}$

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) $\log_a{\bigl(a^2\sqrt{a}\,\bigr)}$

Övning 3.3:4

Förenkla

a) $\lg{50}-\lg{5}$ b) $\lg{23}+\lg{\displaystyle \frac{1}{23}}$ c) $\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}$

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) $\left(e^{\ln{e}}\right)^2$

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) $\log_3{\log_2{(3^{118})}}$
d) $\sqrt7$
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