Question

evaluate the logarithm without the use of a calculator. \\(\log_{5} 125 = \square\\)

Explanation:

Step1: Recall logarithm definition

Let \( \log_{5}125 = x \). By definition, \( 5^x = 125 \).

Step2: Express 125 as power of 5

We know \( 125 = 5^3 \). So \( 5^x = 5^3 \).

Step3: Solve for x

Since bases are equal, exponents must be equal. Thus, \( x = 3 \).

Answer:

\( 3 \)