Solve 96=a(2)^n-1

$$96 = a ( 2 ) ^ { n - 1 }$$

Solve for a

$$a=\frac{192}{2^{n}}$$

Steps for Solving Linear Equation

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

$$a\times 2^{n-1}=96$$

The equation is in standard form.

$$2^{n-1}a=96$$

Divide both sides by 2^{n-1}.

$$\frac{2^{n-1}a}{2^{n-1}}=\frac{96}{2^{n-1}}$$

Dividing by 2^{n-1} undoes the multiplication by 2^{n-1}.

$$a=\frac{96}{2^{n-1}}$$

Divide 96 by 2^{n-1}.

$$a=\frac{192}{2^{n}}$$

Solve for n

$$n=\frac{-\ln(a)+\ln(192)}{\ln(2)}$$

$$a>0$$