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Övningar 3.3

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Versionen från 16 juli 2007 kl. 08.09 (redigera)
KTH.SE:u1zpa8nw (Diskussion | bidrag)
(Ny sida: __NOTOC__ ==&Ouml;vning 3.3:1== <div class="ovning"> Best&auml;m \,x\, om <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="50%"...)
← Gå till föregående ändring		 Versionen från 16 juli 2007 kl. 11.26 (redigera) (ogör)
KTH.SE:u1zpa8nw (Diskussion | bidrag)

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Rad 1: Rad 1:
__NOTOC__ __NOTOC__
-==&Ouml;vning 3.3:1==+'''&Ouml;vning 3.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Best&auml;m \,x\, om Best&auml;m \,x\, om
-<table width="100%" cellspacing="10px">+<table width="100%" style="margin-top:-20px; margin-bottom:-5px;">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">10^x=1\,000</td> <td class="ntext" width="50%">10^x=1\,000</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">10^x=0{,}1</td> <td class="ntext" width="50%">10^x=0{,}1</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">\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>
Rad 20: Rad 20:
</div> </div>
-==&Ouml;vning 3.3:2==+'''&Ouml;vning 3.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Ber&auml;kna Ber&auml;kna
-<table width="100%" cellspacing="10px">+<table width="100%" style="margin-top:-20px; margin-bottom:-5px;">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">\lg{ 0{,}1}</td> <td class="ntext" width="25%">\lg{ 0{,}1}</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">\lg{ 10\,000}</td> <td class="ntext" width="25%">\lg{ 10\,000}</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">\lg {0{,}001}</td> <td class="ntext" width="25%">\lg {0{,}001}</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">\lg {1}</td> <td class="ntext" width="25%">\lg {1}</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">10^{\lg{2}}</td> <td class="ntext" width="25%">10^{\lg{2}}</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">\lg{10^3}</td> <td class="ntext" width="25%">\lg{10^3}</td>
-<td class="ntext">g)</td>+<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">10^{-\lg{0{,}1}}</td> <td class="ntext" width="25%">10^{-\lg{0{,}1}}</td>
-<td class="ntext">h)</td>+<td class="ntext">h)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">\lg{\displaystyle \frac{1}{10^2}}</td> <td class="ntext" width="25%">\lg{\displaystyle \frac{1}{10^2}}</td>
</tr> </tr>
Rad 48: Rad 48:
</div> </div>
-==&Ouml;vning 3.3:3==+'''&Ouml;vning 3.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Ber&auml;kna Ber&auml;kna
-<table width="100%" cellspacing="10px">+<table width="100%" style="margin-top:-20px; margin-bottom:-5px;">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\log_2{8}</td> <td class="ntext" width="33%">\log_2{8}</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\log_2{0{,}125}</td> <td class="ntext" width="33%">\log_2{0{,}125}</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\log_3{\left(9\cdot3^{1/3}\right)}</td> <td class="ntext" width="33%">\log_3{\left(9\cdot3^{1/3}\right)}</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">2^{\log_{\scriptstyle2}{4}}</td> <td class="ntext" width="33%">2^{\log_{\scriptstyle2}{4}}</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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>
<tr align="left"> <tr align="left">
-<td class="ntext">g)</td>+<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</td> <td class="ntext" width="33%">\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</td>
</tr> </tr>
Rad 78: Rad 78:
</div> </div>
-==&Ouml;vning 3.3:4==+'''&Ouml;vning 3.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
F&ouml;renkla F&ouml;renkla
-<table width="100%" cellspacing="10px">+<table width="100%" style="margin-top:-20px; margin-bottom:-5px;">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\lg{50}-\lg{5}</td> <td class="ntext" width="33%">\lg{50}-\lg{5}</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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>
Rad 94: Rad 94:
</div> </div>
-==&Ouml;vning 3.3:5==+'''&Ouml;vning 3.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
F&ouml;renkla F&ouml;renkla
-<table width="100%" cellspacing="10px">+<table width="100%" style="margin-top:-20px; margin-bottom:-5px;">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">(\ln{1})\cdot e^2</td> <td class="ntext" width="33%">(\ln{1})\cdot e^2</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\ln{e}-1</td> <td class="ntext" width="33%">\ln{e}-1</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">\left(e^{\ln{e}}\right)^2</td> <td class="ntext" width="33%">\left(e^{\ln{e}}\right)^2</td>
</tr> </tr>
Rad 118: Rad 118:
</div> </div>
-==&Ouml;vning 3.3:6==+'''&Ouml;vning 3.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
[[Bild:miniraknare.gif||right]] [[Bild:miniraknare.gif||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''): 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%" >
<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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">\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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">\log_3{\log_2{(3^{118})}}</td> <td class="ntext" width="100%">\log_3{\log_2{(3^{118})}}</td>
</tr> </tr>

Versionen från 16 juli 2007 kl. 11.26

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})}}
Den här artikeln är hämtad från http://wiki.math.se/wikis/sf0600_0701/index.php/%C3%96vningar_3.3
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