Find All Complex Solutions 2^(x+3)+2^x=72

$2^{x + 3} + 2^{x} = 72$

Step 1

Factor out $2^{x}$ from the expression.

$2^{x} (8 + 1)$

Step 2

Add $8$ and $1$ .

$2^{x} \cdot 9 = 72$

Step 3

Move $9$ to the left of $2^{x}$ .

$9 \cdot 2^{x} = 72$

Step 4

Divide each term in $(9 \cdot 2^{x}) = 72$ by $9$ and simplify.

Divide each term in $(9 \cdot 2^{x}) = 72$ by $9$ .

$\frac{(9 \cdot 2^{x})}{9} = \frac{72}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 \cdot 2^{x}}{9} = \frac{72}{9}$

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

$2^{x} = \frac{72}{9}$

Simplify the right side.

Divide $72$ by $9$ .

$2^{x} = 8$

Step 5

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

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

Step 6

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

$x = 3$