Solve for x 4^x=8^3

$4^{x} = 8^{3}$

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

$2^{2 x} = 2^{3 \cdot 3}$

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

$2 x = 3 \cdot 3$

Solve for $x$ .

Multiply $3$ by $3$ .

$2 x = 9$

Divide each term in $2 x = 9$ by $2$ and simplify.

Divide each term in $2 x = 9$ by $2$ .

$\frac{2 x}{2} = \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{9}{2}$

Divide $x$ by $1$ .

$x = \frac{9}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{2}$

Decimal Form:

$x = 4.5$

Mixed Number Form:

$x = 4 \frac{1}{2}$