Solve 5^{2x} = 25 for x.

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Multiple Choice

Solve 5^{2x} = 25 for x.

Explanation:
You solve by noticing the bases are the same. Rewrite 25 as 5^2, so you have 5^{2x} = 5^2. When the bases are equal, the exponents must be equal, giving 2x = 2, which leads to x = 1. Only this value makes the two powers match. Quick checks show other candidates don’t produce 25 (for example, x = 0 gives 5^0 = 1, and x = 2 gives 5^4 = 625). So the solution is x = 1.

You solve by noticing the bases are the same. Rewrite 25 as 5^2, so you have 5^{2x} = 5^2. When the bases are equal, the exponents must be equal, giving 2x = 2, which leads to x = 1. Only this value makes the two powers match. Quick checks show other candidates don’t produce 25 (for example, x = 0 gives 5^0 = 1, and x = 2 gives 5^4 = 625). So the solution is x = 1.

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