Solve 2^s=128

$$2 ^ { s } = 128$$

Solve for s

$$s=7$$

Steps Using Definition of Logarithm

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

$$2^{s}=128$$

Take the logarithm of both sides of the equation.

$$\log(2^{s})=\log(128)$$

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

$$s\log(2)=\log(128)$$

Divide both sides by \log(2).

$$s=\frac{\log(128)}{\log(2)}$$

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

$$s=\log_{2}\left(128\right)$$