Solve for x 3^(x+3)-3^(x+2)=162

$3^{x + 3} - 3^{x + 2} = 162$

Step 1

Factor out $3^{x + 2}$ from the expression.

$3^{x + 2} (3 - 1)$

Step 2

Subtract $1$ from $3$ .

$3^{x + 2} \cdot 2 = 162$

Step 3

Move $2$ to the left of $3^{x + 2}$ .

$2 \cdot 3^{x + 2} = 162$

Step 4

Divide each term in $(2 \cdot 3^{x + 2}) = 162$ by $2$ and simplify.

Divide each term in $(2 \cdot 3^{x + 2}) = 162$ by $2$ .

$\frac{(2 \cdot 3^{x + 2})}{2} = \frac{162}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 3^{x + 2}}{2} = \frac{162}{2}$

Divide $3^{x + 2}$ by $1$ .

$3^{x + 2} = \frac{162}{2}$

Simplify the right side.

Divide $162$ by $2$ .

$3^{x + 2} = 81$

Step 5

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

$3^{x + 2} = 3^{4}$

Step 6

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

$x + 2 = 4$

Step 7

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

Subtract $2$ from both sides of the equation.

$x = 4 - 2$

Subtract $2$ from $4$ .

$x = 2$