Question

If \( 7^{\frac{x}{3}} = 2401 \), then the value of \( x \) is:

• A. 9
• B. 10
• C. 12
• D. 15

Hint:

When solving equations with the same base, equate the exponents directly.

Answer 1

The Correct Option is C

We are given the equation \( 7^{\frac{x}{3}} = 2401 \). First, express 2401 as a power of 7: \[ 2401 = 7^4 \] Thus, the equation becomes: \[ 7^{\frac{x}{3}} = 7^4 \] Since the bases are the same, we can equate the exponents: \[ \frac{x}{3} = 4 \] Multiplying both sides by 3: \[ x = 4 \times 3 = 12 \] Thus, the value of \( x \) is 12.