Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$x = - 2$