Solve 4590=18*(2^k-1)

$$4590 = 18 * ( 2 ^ { k } - 1 )$$

Solve for k

$$k=8$$

Steps Using Definition of Logarithm

Divide both sides by 18.

$$\frac{4590}{18}=2^{k}-1$$

Divide 4590 by 18 to get 255.

$$255=2^{k}-1$$

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

$$2^{k}-1=255$$

Add 1 to both sides of the equation.

$$2^{k}=256$$

Take the logarithm of both sides of the equation.

$$\log(2^{k})=\log(256)$$

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

$$k\log(2)=\log(256)$$

Divide both sides by \log(2).

$$k=\frac{\log(256)}{\log(2)}$$

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

$$k=\log_{2}\left(256\right)$$