Solve for x 64^x=32

$64^{x} = 32$

Step 1

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

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

Step 2

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

$6 x = 5$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.8\overline{3}$