Solve 52=4^x-12

$$52= { 4 }^{ x } -12$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$4^{x}-12=52$$

Add 12 to both sides of the equation.

$$4^{x}=64$$

Take the logarithm of both sides of the equation.

$$\log(4^{x})=\log(64)$$

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

$$x\log(4)=\log(64)$$

Divide both sides by \log(4).

$$x=\frac{\log(64)}{\log(4)}$$

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

$$x=\log_{4}\left(64\right)$$

Solve for x (complex solution)

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

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