Problem 31 - College Algebra

Question

Evaluate each expression without using a calculator. $$\log _{5} 5$$

Step-by-Step Solution

Answer

The final answer of the expression \(\log _{5} 5\) is 1.

Step 1: Identify the base and the expression of the logarithm

In this problem, \(\log _{5} 5\), 5 is the base, and the expression is also 5.

Step 2: Apply the logarithm rule

Remember that for any base \(b\), \(\log_{b} b = 1\). Hence, \(\log _{5} 5 = 1\) by applying the rule.

Step 3: Write the final answer

From step 2, it follows that \(\log _{5} 5 = 1\).