Solve 3.91^12=2^x

$${ 3.91 }^{ 12 } = { 2 }^{ x }$$

Solve for x

$$x=12\log_{2}\left(3.91\right)\approx 23.60602329$$

Steps Using Definition of Logarithm

Calculate 3.91 to the power of 12 and get 12767947.514633659874603497973281.

$$12767947.514633659874603497973281=2^{x}$$

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

$$2^{x}=12767947.514633659874603497973281$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(12767947.514633659874603497973281)$$

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

$$x\log(2)=\log(12767947.514633659874603497973281)$$

Divide both sides by \log(2).

$$x=\frac{\log(12767947.514633659874603497973281)}{\log(2)}$$

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

$$x=\log_{2}\left(12767947.514633659874603497973281\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+2\log_{2}\left(3573.226485213841\right)$$

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