Solution 3.3:2g

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We know that
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<math>10^{\lg x}=x</math>, so therefore we rewrite the exponent as
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<math>-\lg 0.1=\left( -1 \right)\centerdot \lg 0.1=\lg 0.1^{-1}</math>
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by using the log law
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<math>b\lg a=\lg a^{b}</math>. This gives
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<math>10^{-\lg 0.1}=10^{\lg 0.1^{-1}}=0.1^{-1}=\frac{1}{0.1}=10</math>

Revision as of 13:31, 25 September 2008

We know that \displaystyle 10^{\lg x}=x, so therefore we rewrite the exponent as \displaystyle -\lg 0.1=\left( -1 \right)\centerdot \lg 0.1=\lg 0.1^{-1} by using the log law \displaystyle b\lg a=\lg a^{b}. This gives


\displaystyle 10^{-\lg 0.1}=10^{\lg 0.1^{-1}}=0.1^{-1}=\frac{1}{0.1}=10

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