/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 Evaluate each expression without... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 37

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

Short Answer

Expert verified
The value of \(\log_4 1\) is 0.

Step by step solution

01

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.
02

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.
03

Evaluating \(\log_4 1\)

Therefore, \(\log_4 1 = 0\) because \(4^0 = 1\)

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