Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. \[ 5^{2 x-11}=125 \] The solution set is

Step 1 ：Express both sides of the equation as powers of the same base. We know that 5 and 125 can both be expressed as powers of 5. So, we can rewrite 125 as \(5^3\).

Step 2 ：Equating the exponents, we get \(2x - 11 = 3\).

Step 3 ：Solving for \(x\), we get \(x = 7\).

Step 4 ：The solution set is \(\boxed{7}\).