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

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 \(\boxed{4}\)