Solve the equation.
\[
25^{x}=5
\]

The solution set is \{\} .
(Type an integer or a simplified fraction.)

Answer

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Answer

Final Answer: The solution set is \(\boxed{\frac{1}{2}}\)

Steps

Step 1 ：Given the equation \(25^{x}=5\)

Step 2 ：We know that 25 is 5 squared, so we can rewrite the equation as \((5^2)^x = 5\)

Step 3 ：Using the rule of exponents \((a^{m*n}) = (a^m)^n\), we can simplify the left side of the equation to \(5^{2x} = 5\)

Step 4 ：Since the bases are equal, we can equate the exponents. This gives us \(2x = 1\)

Step 5 ：Solving for x, we get \(x = \frac{1}{2}\)

Step 6 ：Final Answer: The solution set is \(\boxed{\frac{1}{2}}\)