Question

The value of \( \log_5 \left( \frac{1}{125} \right) \) is:

• A. 5
• B. 3
• C. -3
• D. 0

Hint:

When dealing with logarithms, remember that \( \log_b a^n = n \log_b a \), and use properties of exponents to simplify the expression.

Answer 1

The Correct Option is C

We are asked to find \( \log_5 \left( \frac{1}{125} \right) \). First, express 125 as a power of 5: \[ 125 = 5^3 \] Therefore: \[ \log_5 \left( \frac{1}{125} \right) = \log_5 \left( 5^{-3} \right) \] Using the logarithmic property \( \log_b \left( a^n \right) = n \log_b a \): \[ \log_5 \left( 5^{-3} \right) = -3 \] Thus, the correct answer is \( -3 \).