Solve for x 125^x=5

$125^{x} = 5$

Step 1

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

$5^{3 x} = 5^{1}$

Step 2

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

$3 x = 1$

Step 3

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$