Solve for x 96=3(2^(x+2))

$96 = 3 (2^{x + 2})$

Step 1

Rewrite the equation as $3 \cdot 2^{x + 2} = 96$ .

$3 \cdot 2^{x + 2} = 96$

Step 2

Divide each term in $(3 \cdot 2^{x + 2}) = 96$ by $3$ and simplify.

Divide each term in $(3 \cdot 2^{x + 2}) = 96$ by $3$ .

$\frac{(3 \cdot 2^{x + 2})}{3} = \frac{96}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \cdot 2^{x + 2}}{3} = \frac{96}{3}$

Divide $2^{x + 2}$ by $1$ .

$2^{x + 2} = \frac{96}{3}$

Simplify the right side.

Divide $96$ by $3$ .

$2^{x + 2} = 32$

Step 3

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

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

Step 4

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

$x + 2 = 5$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$x = 5 - 2$

Subtract $2$ from $5$ .

$x = 3$