Solve for x 2^x=1/8

$2^{x} = \frac{1}{8}$

Step 1

Raise $8$ to the power of $1$ .

$2^{x} = \frac{1}{8^{1}}$

Step 2

Move $8^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x} = 8^{- 1}$

Step 3

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

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

Step 4

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

$x = - 3$