Solve 2^2x-6=12Rightarrowa/b=?

$$2 ^ { 2 x - 6 } = 12 \Rightarrow \frac { a } { b } = ?$$

Solve for x

$$x = \frac{\log_{2} {(3)} + 8}{2} \approx 4.79248125$$

Steps Using Definition of Logarithm

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

$$2^{2x-6}=12$$

Take the logarithm of both sides of the equation.

$$\log(2^{2x-6})=\log(12)$$

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

$$\left(2x-6\right)\log(2)=\log(12)$$

Divide both sides by \log(2).

$$2x-6=\frac{\log(12)}{\log(2)}$$

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

$$2x-6=\log_{2}\left(12\right)$$

Add 6 to both sides of the equation.

$$2x=\log_{2}\left(12\right)-\left(-6\right)$$

Divide both sides by 2.

$$x=\frac{\log_{2}\left(12\right)+6}{2}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(3\right)}{2}+4$$

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