Problem 37
Question
Evaluate each expression without using a calculator. $$\log _{4} 1$$
Step-by-Step Solution
Verified Answer
The value of \(\log_4 1\) is 0.
1Step 1: Recall the property of Logarithms
Any number (except zero), raised to the power 0, equals 1. This is written mathematically as \(a^0 = 1\), where \(a\) can be any number except zero.
2Step 2: Apply this property to the given Logarithm
We have a logarithm with base 4 and the number is 1, i.e., \(\log_4 1\). Let's find a power to which 4 can be raised to get 1. With the property recalled in the previous step, 4 raised to the power 0 gives 1.
3Step 3: Evaluating \(\log_4 1\)
Therefore, \(\log_4 1 = 0\) because \(4^0 = 1\)
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