We are asked to solve the equation $5^{2x+1} = 125$ for the value of $x$.

1. Problem Description

We are asked to solve the equation $5^{2x+1} = 125$ for the value of $x$.

2. Solution Steps

First, we express 125 as a power of

5. Since $125 = 5 \times 5 \times 5 = 5^3$, we have:

$5^{2x+1} = 5^3$

Since the bases are equal, the exponents must be equal.

Therefore, we can write:

$2x+1 = 3$

Next, subtract 1 from both sides of the equation:

$2x+1-1 = 3-1$

$2x = 2$

Finally, divide both sides of the equation by 2 to solve for $x$:

$\frac{2x}{2} = \frac{2}{2}$

$x = 1$

3. Final Answer

The solution to the equation $5^{2x+1} = 125$ is $x=1$.