Solve for x: 5^2x−1=125

Question

(1 point)
x=

Answer 1

To solve the equation \( 5^{2x - 1} = 125 \), we first express \( 125 \) as a power of \( 5 \).

We know that:

\[ 125 = 5^3 \]

Now we can rewrite the equation:

\[ 5^{2x - 1} = 5^3 \]

Since the bases are the same, we can set the exponents equal to each other:

\[ 2x - 1 = 3 \]

Now, solve for \( x \):

1. Add \( 1 \) to both sides:

\[ 2x = 3 + 1 \] \[ 2x = 4 \]

2. Divide both sides by \( 2 \):

\[ x = \frac{4}{2} \] \[ x = 2 \]

Thus, the solution is:

\[ \boxed{2} \]