Solve 2^n-1=4

$$2 ^ { n - 1 } = 4$$

Solve for n

$$n=3$$

Steps Using Definition of Logarithm

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

$$2^{n-1}=4$$

Take the logarithm of both sides of the equation.

$$\log(2^{n-1})=\log(4)$$

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

$$\left(n-1\right)\log(2)=\log(4)$$

Divide both sides by \log(2).

$$n-1=\frac{\log(4)}{\log(2)}$$

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

$$n-1=\log_{2}\left(4\right)$$

Add 1 to both sides of the equation.

$$n=2-\left(-1\right)$$