Multiple Choice
Evaluate the given logarithm.
11. Inverse, Exponential, & Logarithmic Functions
Introduction to Logarithmic Functions
Multiple Choice
Evaluate the given logarithmic expression.
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Verified step by step guidance1
Recall the definition of a logarithm: \(\log_{b} a = c\) means that \(b^{c} = a\). Here, we want to find \(\log_{10} 0.1\), so we are looking for the exponent \(c\) such that \$10^{c} = 0.1$.
Express 0.1 as a power of 10. Since 0.1 is the same as \(\frac{1}{10}\), rewrite it as \$10^{-1}$.
Substitute this back into the equation: \$10^{c} = 10^{-1}$.
Since the bases are the same (both 10), set the exponents equal to each other: \(c = -1\).
Therefore, \(\log_{10} 0.1 = -1\). This shows how logarithms convert multiplication and division into addition and subtraction of exponents.
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