Question

Find the value of \( \log_3 81 \).

• A. 3
• B. 4
• C. 2
• D. 1

Hint:

Remember: The logarithmic property \( \log_b (b^n) = n \) is useful when the argument of the logarithm is a power of the base.

Answer 1

The Correct Option is B

Step 1: Express 81 as a power of 3 We know that: \[ 81 = 3^4 \] Step 2: Use the logarithmic identity We use the logarithmic identity \( \log_b a^n = n \log_b a \), so: \[ \log_3 81 = \log_3 (3^4) \] Step 3: Apply the logarithmic rule By applying the rule \( \log_b (b^n) = n \), we get: \[ \log_3 (3^4) = 4 \] Answer: Therefore, \( \log_3 81 = 4 \). So, the correct answer is option (2).