Solve for x 3(4)^x=96

$3 {(4)}^{x} = 96$

Divide each term in $(3 \cdot 4^{x}) = 96$ by $3$ and simplify.

Divide each term in $(3 \cdot 4^{x}) = 96$ by $3$ .

$\frac{(3 \cdot 4^{x})}{3} = \frac{96}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \cdot 4^{x}}{3} = \frac{96}{3}$

Divide $4^{x}$ by $1$ .

$4^{x} = \frac{96}{3}$

Simplify the right side.

Divide $96$ by $3$ .

$4^{x} = 32$

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

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

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

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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