Questions: Evaluate the expression without using a calculator. log4 1

Evaluate the expression without using a calculator. log4 1
Transcript text: Evaluate the expression without using a calculator. \[ \log _{4} 1 \]
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Solution

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Solution Steps

Step 1: Understanding Logarithms

The logarithm \(\log_{b} a\) answers the question: "To what power must \(b\) be raised, to yield \(a\)?"

Step 2: Special Cases

Since \(a = 1\), regardless of the base \(b\), \(\log_{b} 1 = 0\) because any non-1 base raised to the power of 0 equals 1.

Step 3: Calculation

The answer is derived directly from the special cases: 0.

Final Answer: The value of \(\log_{4} 1\) rounded to 0 decimal places is 0.

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