Question:
If \( 7^{\frac{x}{3}} = 2401 \), then the value of \( x \) is:
If \( 7^{\frac{x}{3}} = 2401 \), then the value of \( x \) is:
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When solving equations with the same base, equate the exponents directly.
Updated On: Feb 16, 2025
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The Correct Option is C
Solution and Explanation
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.
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