Multiple Choice
Evaluate the given expression.
13. 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 means we want to find the exponent \( x \) such that \( 5^x = \frac{1}{125} \).
Rewrite \( \frac{1}{125} \) as a power of 5. Since \( 125 = 5^3 \), then \( \frac{1}{125} = 5^{-3} \).
Substitute this back into the logarithmic equation: \( \log_5 \left( 5^{-3} \right) \).
Use the logarithmic identity \( \log_b (b^k) = k \) to simplify the expression to \( -3 \).
Therefore, the value of \( \log_5 \left( \frac{1}{125} \right) \) is \( -3 \).
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