Precalculus Examples

$\frac{1}{16} = 4^{x}$

Step 1

Rewrite the equation as $4^{x} = \frac{1}{16}$ .

$4^{x} = \frac{1}{16}$

Step 2

Raise $16$ to the power of $1$ .

$4^{x} = \frac{1}{16^{1}}$

Step 3

Move $16^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$4^{x} = 16^{- 1}$

Step 4

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

$4^{x} = 4^{- 2}$

Step 5

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

$x = - 2$