Solve for x 25^(2x)=125^(x+2)

$25^{2 x} = 125^{x + 2}$

Step 1

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

$5^{2 (2 x)} = 5^{3 (x + 2)}$

Step 2

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

$2 (2 x) = 3 (x + 2)$

Step 3

Solve for $x$ .

Multiply $2$ by $2$ .

$4 x = 3 (x + 2)$

Simplify $3 (x + 2)$ .

Apply the distributive property.

$4 x = 3 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$4 x = 3 x + 6$

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$4 x - 3 x = 6$

Subtract $3 x$ from $4 x$ .

$x = 6$