Solution 3.3:3c

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First, we rewrite the number
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<center> [[Image:3_3_3c.gif]] </center>
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<math>0.\text{125 }</math>
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as a fraction which we also simplify:
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<math>0.\text{125 }=\frac{\text{125 }}{1000}=\frac{5\centerdot 25}{10^{3}}=\frac{5\centerdot 5\centerdot 5}{\left( 2\centerdot 5 \right)^{3}}=\frac{1}{2^{3}}=2^{-3}</math>
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Because
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<math>0.\text{125 }</math>
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was expressed as a power of
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<math>\text{2}</math>, the logarithm can be calculated in full:
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<math>\log _{2}0.\text{125 }=\log _{2}2^{-3}=\left( -3 \right)\centerdot \log _{2}2=\left( -3 \right)\centerdot 1=-3</math>

Revision as of 14:13, 25 September 2008

First, we rewrite the number \displaystyle 0.\text{125 } as a fraction which we also simplify:


\displaystyle 0.\text{125 }=\frac{\text{125 }}{1000}=\frac{5\centerdot 25}{10^{3}}=\frac{5\centerdot 5\centerdot 5}{\left( 2\centerdot 5 \right)^{3}}=\frac{1}{2^{3}}=2^{-3}


Because \displaystyle 0.\text{125 } was expressed as a power of \displaystyle \text{2}, the logarithm can be calculated in full:


\displaystyle \log _{2}0.\text{125 }=\log _{2}2^{-3}=\left( -3 \right)\centerdot \log _{2}2=\left( -3 \right)\centerdot 1=-3

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