Evaluate 5^(3x+2)=625

$5^{3 x + 2} = 625$

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

$5^{3 x + 2} = 5^{4}$

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

$3 x + 2 = 4$

Solve for $x$ .

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

Subtract $2$ from both sides of the equation.

$3 x = 4 - 2$

Subtract $2$ from $4$ .

$3 x = 2$

Divide each term in $3 x = 2$ by $3$ and simplify.

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$