Solve for n 5^(3n)=125

$5^{3 n} = 125$

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

$5^{3 n} = 5^{3}$

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

$3 n = 3$

Divide each term in $3 n = 3$ by $3$ and simplify.

Divide each term in $3 n = 3$ by $3$ .

$\frac{3 n}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} = \frac{3}{3}$

Divide $n$ by $1$ .

$n = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$n = 1$