Solve 2^n=188

$$2 ^ { n } = 188$$

Solve for n

$$n=\log_{2}\left(188\right)\approx 7.554588852$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$2^{n}=188$$

Take the logarithm of both sides of the equation.

$$\log(2^{n})=\log(188)$$

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

$$n\log(2)=\log(188)$$

Divide both sides by \log(2).

$$n=\frac{\log(188)}{\log(2)}$$

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

$$n=\log_{2}\left(188\right)$$