Solve 1/8=2^n

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

Solve for n

$$n=-3$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

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

Take the logarithm of both sides of the equation.

$$\log(2^{n})=\log(\frac{1}{8})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$n\log(2)=\log(\frac{1}{8})$$

Divide both sides by \log(2).

$$n=\frac{\log(\frac{1}{8})}{\log(2)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$n=\log_{2}\left(\frac{1}{8}\right)$$