Solve for x 8^x=1/4

$8^{x} = \frac{1}{4}$

Step 1

Raise $4$ to the power of $1$ .

$8^{x} = \frac{1}{4^{1}}$

Step 2

Move $4^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$8^{x} = 4^{- 1}$

Step 3

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

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

Step 4

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

$3 x = - 2$

Step 5

Divide each term in $3 x = - 2$ by $3$ and simplify.

Divide each term in $3 x = - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2}{3}$

Divide $x$ by $1$ .

$x = \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}$

Decimal Form:

$x = - 0.\overline{6}$