Problem 37 - Introductory and Intermediate Algebra for College Students 4th

Question

Evaluate each expression without using a calculator. $$\log _{4} 1$$

Step-by-Step Solution

Answer

\(\log _{4} 1 = 0\).

Step 1: Understand the Problem

We are asked to evaluate \(\log _{4} 1\). We need to find a number that when raised to the power 4 equals 1.

Step 2: Apply the Logarithmic Property

Recall that \(\log _{b} a = c\) means \(b^c=a\). Now we need to find a number c so that \(4^c=1\). By convention, any number to the power of 0 is equal to 1. Therefore, the number c we're looking for is 0.

Step 3: Write down the Solution

Therefore, \(\log _{4} 1 = 0 \), because \(4^0=1\).