Precalculus Examples

$3^{x + 2} = \frac{1}{9}$

Step 1

Raise $9$ to the power of $1$ .

$3^{x + 2} = \frac{1}{9^{1}}$

Step 2

Move $9^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x + 2} = 9^{- 1}$

Step 3

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

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

Step 4

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

$x + 2 = - 2$

Step 5

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

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Step 5.1

Subtract $2$ from both sides of the equation.

$x = - 2 - 2$

Step 5.2

Subtract $2$ from $- 2$ .

$x = - 4$