Question

The value of $\log_7 343$ is “‘latex id="m22nlf"

• A. 8
• B. 5
• C. 3
• D. 6

Hint:

If the number is a power of the base, the logarithm directly gives the exponent. Always rewrite numbers in exponential form first.

Answer 1

The Correct Option is C

Concept: A logarithm answers the question: “What power should the base be raised to in order to get the given number?” Key identity: \[ \log_b(b^n) = n \]

Step 1: Express 343 as a power of 7. \[ 7^1 = 7,\quad 7^2 = 49,\quad 7^3 = 343 \] So, \[ 343 = 7^3 \]

Step 2: Rewrite the logarithm. \[ \log_7 343 = \log_7(7^3) \]

Step 3: Apply logarithmic identity. \[ \log_7(7^3) = 3 \] Final Answer: \[ \boxed{3} \]