Multiple Choice
Evaluate the given expression.
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
Recognize that the expression is \( \log_5 \left( \frac{1}{125} \right) \), which asks for the exponent to which 5 must be raised to get \( \frac{1}{125} \).
Rewrite \( \frac{1}{125} \) as a power of 5. Since \( 125 = 5^3 \), then \( \frac{1}{125} = 5^{-3} \).
Substitute this back into the logarithm: \( \log_5 \left( 5^{-3} \right) \).
Use the logarithm power rule: \( \log_b (b^x) = x \), so \( \log_5 \left( 5^{-3} \right) = -3 \).
Therefore, the value of the logarithmic expression is \( -3 \).
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