Solve for x 32^x=64

$32^{x} = 64$

Step 1

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

$2^{5 x} = 2^{6}$

Step 2

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

$5 x = 6$

Step 3

Divide each term in $5 x = 6$ by $5$ and simplify.

Divide each term in $5 x = 6$ by $5$ .

$\frac{5 x}{5} = \frac{6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{6}{5}$

Divide $x$ by $1$ .

$x = \frac{6}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{5}$

Decimal Form:

$x = 1.2$

Mixed Number Form:

$x = 1 \frac{1}{5}$