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Chapter 12: Problem 37

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

Short Answer

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

Step by step solution

01

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.
02

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.
03

Write down the Solution

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

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Most popular questions from this chapter

Describe the quotient rule for logarithms and give an example.

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