Question

The value of \( \log_3 81 \) is:

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

To solve logarithms of powers, express the number as a power of the base and apply the logarithmic rule \( \log_b b^n = n \).

Answer 1

The Correct Option is C

We are asked to find the value of \( \log_3 81 \), which means we need to determine the exponent to which the base 3 must be raised to produce 81. Step 1: Write 81 as a power of 3: \[ 81 = 3^4. \] Step 2: Thus, \[ \log_3 81 = \log_3 3^4. \] Step 3: Using the logarithmic property \( \log_b (a^n) = n \log_b a \), we get: \[ \log_3 3^4 = 4. \] Thus, the value of \( \log_3 81 \) is \( 4 \).