Algebra Examples

$3^{x + 2} - 3^{x + 1} = 18$

Step 1

Factor out $3^{x + 1}$ from the expression.

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

Step 2

Subtract $1$ from $3$ .

$3^{x + 1} \cdot 2 = 18$

Step 3

Move $2$ to the left of $3^{x + 1}$ .

$2 \cdot 3^{x + 1} = 18$

Step 4

Divide each term in $2 \cdot 3^{x + 1} = 18$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 \cdot 3^{x + 1} = 18$ by $2$ .

$\frac{2 \cdot 3^{x + 1}}{2} = \frac{18}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 \cdot 3^{x + 1}}{2} = \frac{18}{2}$

Step 4.2.1.2

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

$3^{x + 1} = \frac{18}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $18$ by $2$ .

$3^{x + 1} = 9$

Step 5

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

$3^{x + 1} = 3^{2}$

Step 6

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

$x + 1 = 2$

Step 7

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

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Step 7.1

Subtract $1$ from both sides of the equation.

$x = 2 - 1$

Step 7.2

Subtract $1$ from $2$ .

$x = 1$