Solve for x 5^(2x-5)=125

$5^{2 x - 5} = 125$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$5^{2 x - 5} = 5^{3}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x - 5 = 3$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $5$ to both sides of the equation.

$2 x = 3 + 5$

Add $3$ and $5$ .

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$