Problem 37
Question
Evaluate each expression without using a calculator. $$\log _{4} 1$$
Step-by-Step Solution
Verified Answer
0
1Step 1: Understanding the problem
Given expression is \( \log _{4} 1 \). The logarithm base 4 of 1 represents the power or exponent to which 4 must be raised to get 1.
2Step 2: Apply the logarithmic rule
One of the basic facts about logarithms is that any number (except 0) raised to the power of 0 equals 1. That is, if a^0 = 1, then log_a(1) = 0, where a is the base.
3Step 3: Evaluate the expression
Therefore, applying this rule to our expression, \( \log _{4} 1 \) is equal to 0.
Other exercises in this chapter
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Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
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Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution