Solve 2^2x-(-6)=96

$$2 ^ { 2 x } - ( - 6 ) = 96$$

Solve for x

$$x = \frac{\log_{2} {(90)}}{2} \approx 3.245926548$$

Steps Using Definition of Logarithm

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

$$2^{2x}+6=96$$

Subtract 6 from both sides of the equation.

$$2^{2x}=90$$

Take the logarithm of both sides of the equation.

$$\log(2^{2x})=\log(90)$$

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

$$2x\log(2)=\log(90)$$

Divide both sides by \log(2).

$$2x=\frac{\log(90)}{\log(2)}$$

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

$$2x=\log_{2}\left(90\right)$$

Divide both sides by 2.

$$x=\frac{\log_{2}\left(90\right)}{2}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(90\right)}{2}$$

$$n_{1}\in \mathrm{Z}$$