Problem 35 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The value of the expression \(\log_5 5\) is 1.

Step 1: Understand the Logarithm Definition

A logarithm, usually written as \(\log_b a\), transforms from an exponential form to a logarithmic form. It basically asks the question: to what power should we raise the base (b) to get a? So when the base and the value are equal, the result is 1, as any number raised to the power of 1 gives itself.

Step 2: Apply the Logarithm Definition

Following the definition, we can apply it to \(\log_5 5\). Here, base \(b\) is 5 and \(a\) is also 5. We have to find to what power we need to raise 5 (base) to get 5. Any number raised to the power of 1 is itself, therefore, \(5^1 = 5\), so the answer here will be 1.