Exponent comparison via square roots: If √2401 = √(7^x), find the value of x.

Introduction / Context:
This question connects square roots with exponent rules. Recognizing perfect powers streamlines the solution.

Given Data / Assumptions:
√2401 = √(7^x).

Concept / Approach:
If √A = √B and both are non-negative, then A = B. Also 2401 = 7^4. Then match exponents.

Step-by-Step Solution:
2401 = 7^4.Thus √2401 = √(7^4) = 7^2 = 49.On the right side: √(7^x) = 7^(x/2).Equate: 7^2 = 7^(x/2) ⇒ x/2 = 2 ⇒ x = 4.

Verification / Alternative check:
Substitute x = 4: √(7^4) = √2401 = 49, consistent.

Why Other Options Are Wrong:
3, 5, 6, 2 produce 7^(x/2) not equal to 49.

Common Pitfalls:
Forgetting that √(a^b) = a^(b/2), or misidentifying 2401 as 49^2 and not linking it to 7^4 properly.

Final Answer:
4