Solve 4096=2^N-1

$$4096 = 2 ^ { N - 1 }$$

Solve for N

$$N=13$$

Steps Using Definition of Logarithm

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

$$2^{N-1}=4096$$

Take the logarithm of both sides of the equation.

$$\log(2^{N-1})=\log(4096)$$

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

$$\left(N-1\right)\log(2)=\log(4096)$$

Divide both sides by \log(2).

$$N-1=\frac{\log(4096)}{\log(2)}$$

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

$$N-1=\log_{2}\left(4096\right)$$

Add 1 to both sides of the equation.

$$N=12-\left(-1\right)$$