Solve for x 625^x=3125

$625^{x} = 3125$

Step 1

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

$5^{4 x} = 5^{5}$

Step 2

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

$4 x = 5$

Step 3

Divide each term in $4 x = 5$ by $4$ and simplify.

Divide each term in $4 x = 5$ by $4$ .

$\frac{4 x}{4} = \frac{5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{5}{4}$

Divide $x$ by $1$ .

$x = \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{4}$

Decimal Form:

$x = 1.25$

Mixed Number Form:

$x = 1 \frac{1}{4}$