Solve (-3)(2)^n-1=-1536

$$( - 3 ) ( 2 ) ^ { n - 1 } = - 1536$$

Solve for n

$$n=10$$

Steps Using Definition of Logarithm

Divide both sides by -3.

$$2^{n-1}=\frac{-1536}{-3}$$

Divide -1536 by -3 to get 512.

$$2^{n-1}=512$$

Take the logarithm of both sides of the equation.

$$\log(2^{n-1})=\log(512)$$

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

$$\left(n-1\right)\log(2)=\log(512)$$

Divide both sides by \log(2).

$$n-1=\frac{\log(512)}{\log(2)}$$

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

$$n-1=\log_{2}\left(512\right)$$

Add 1 to both sides of the equation.

$$n=9-\left(-1\right)$$