Precalculus Examples

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

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

Step 1

Raise

9

$9$ to the power of

1

$1$ .

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

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

Step 2

Move

9^{1}

$9^{1}$ to the numerator using the negative exponent rule

\frac{1}{b^{n}} = b^{- n}

$\frac{1}{b^{n}} = b^{- n}$ .

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

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

Step 3

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

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

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

Step 4

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

x = - 2

$x = - 2$