Find the Roots (Zeros) h(x)=2(3^x)-18

$h (x) = 2 (3^{x}) - 18$

Step 1

Set $2 (3^{x}) - 18$ equal to $0$ .

$2 (3^{x}) - 18 = 0$

Step 2

Solve for $x$ .

Add $18$ to both sides of the equation.

$2 \cdot 3^{x} = 18$

Divide each term in $(2 \cdot 3^{x}) = 18$ by $2$ and simplify.

Divide each term in $(2 \cdot 3^{x}) = 18$ by $2$ .

$\frac{(2 \cdot 3^{x})}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 3^{x}}{2} = \frac{18}{2}$

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

$3^{x} = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$3^{x} = 9$

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

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

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

$x = 2$

Step 3