Solve 2^y=12

$$2 ^ { y } = 12$$

Solve for y

$$y=\log_{2}\left(12\right)\approx 3.584962501$$

Steps Using Definition of Logarithm

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

$$2^{y}=12$$

Take the logarithm of both sides of the equation.

$$\log(2^{y})=\log(12)$$

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

$$y\log(2)=\log(12)$$

Divide both sides by \log(2).

$$y=\frac{\log(12)}{\log(2)}$$

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

$$y=\log_{2}\left(12\right)$$

Solve for y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(12\right)$$

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