Solve for x 8^(2x)=32

$8^{2 x} = 32$

Step 1

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

$2^{3 (2 x)} = 2^{5}$

Step 2

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

$3 (2 x) = 5$

Step 3

Solve for $x$ .

Multiply $2$ by $3$ .

$6 \cdot x = 5$

Divide each term in $(6 \cdot x) = 5$ by $6$ and simplify.

Divide each term in $(6 \cdot x) = 5$ by $6$ .

$\frac{(6 \cdot x)}{6} = \frac{5}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

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:

$x = 0.8\overline{3}$