Precalculus Examples

$4^{x} = \frac{1}{256}$

Step 1

Raise $256$ to the power of $1$ .

$4^{x} = \frac{1}{256^{1}}$

Step 2

Move $256^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$4^{x} = 256^{- 1}$

Step 3

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

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

Step 4

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

$x = - 4$