Find the exact value of the logarithm without using a calculator.
\[
\log _{3} 81
\]

Answer

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Answer

Final Answer: The exact value of the logarithm is \(\boxed{4}\)

Steps

Step 1 ：Given the logarithm expression \(\log _{3} 81\)

Step 2 ：This is asking the question: '3 raised to what power equals 81?'

Step 3 ：We know that \(3^4 = 81\)

Step 4 ：So, the answer should be 4

Step 5 ：Final Answer: The exact value of the logarithm is \(\boxed{4}\)