Basic Math Examples

$3^{x + 1} + 3^{x - 1} = 30$

Step 1

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

$3^{x - 1} (9 + 1)$

Step 2

Add $9$ and $1$ .

$3^{x - 1} \cdot 10 = 30$

Step 3

Move $10$ to the left of $3^{x - 1}$ .

$10 \cdot 3^{x - 1} = 30$

Step 4

Divide each term in $10 \cdot 3^{x - 1} = 30$ by $10$ and simplify.

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Step 4.1

Divide each term in $10 \cdot 3^{x - 1} = 30$ by $10$ .

$\frac{10 \cdot 3^{x - 1}}{10} = \frac{30}{10}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $10$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{10 \cdot 3^{x - 1}}{10} = \frac{30}{10}$

Step 4.2.1.2

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

$3^{x - 1} = \frac{30}{10}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $30$ by $10$ .

$3^{x - 1} = 3$

Step 5

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

$3^{x - 1} = 3^{1}$

Step 6

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

$x - 1 = 1$

Step 7

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

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Step 7.1

Add $1$ to both sides of the equation.

$x = 1 + 1$

Step 7.2

Add $1$ and $1$ .

$x = 2$