Problem 38 - Introductory and Intermediate Algebra for College Students 4th

Question

Evaluate each expression without using a calculator. $$\log _{6} 1$$

Step-by-Step Solution

Answer

0

Step 1: Understand the Logarithmic Function

Any logarithmic function \(\log _{b} a = n\) signifies that the base \(b\) raised to the power of \(n\) equals to \(a\). So, if we can rewrite the equation in this form, we can evaluate the value of \(n\).

Step 2: Apply the Definition of Logarithm

We can re-write \(\log _{6} 1 = n\) as \(6^n = 1\). We know that any non-zero number raised to the power of 0 equals 1. Therefore, the value of \(n\) that satisfies this equation is 0.

Step 3: Result

Therefore, the value of the expression \(\log _{6} 1\) is 0.