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Evaluate the given logarithm.
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13. Inverse, Exponential, & Logarithmic Functions
Introduction to Logarithmic Functions
Multiple Choice
Evaluate the given logarithmic expression.
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검증된 단계별 안내1
Recall the definition of logarithm: \(\log_{a} b = c\) means that \(a^{c} = b\). Here, the base is 10 and the argument is 0.1.
Rewrite 0.1 as a power of 10. Since 0.1 is the same as \(\frac{1}{10}\), it can be written as \(10^{-1}\).
Substitute this back into the logarithm expression: \(\log_{10} (10^{-1})\).
Use the logarithm power rule: \(\log_{a} (a^{k}) = k\). Applying this, \(\log_{10} (10^{-1}) = -1\).
Therefore, the value of \(\log_{10} 0.1\) is the exponent to which 10 must be raised to get 0.1, which is \(-1\).
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