Question

solve the equation.
$5^{2x + 1} = 125$

the solution set is {}.
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Express 125 as a power of 5

We know that \(125 = 5^3\), so the equation \(5^{2x + 1}=125\) can be rewritten as \(5^{2x + 1}=5^3\).

Step2: Set the exponents equal

Since the bases are the same (both are 5) and the equation holds, we can set the exponents equal to each other. That is, \(2x + 1 = 3\).

Step3: Solve for x

Subtract 1 from both sides of the equation: \(2x=3 - 1\), which simplifies to \(2x = 2\). Then divide both sides by 2: \(x=\frac{2}{2}=1\).

Answer:

\(\{1\}\)