Algebra Examples

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

Step 1

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

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

Step 2

Solve for $x$ .

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Step 2.1

Add $18$ to both sides of the equation.

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.1.2

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

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

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $18$ by $2$ .

$3^{x} = 9$

Step 2.3

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

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

Step 2.4

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

$x = 2$

Step 3