Solve 4^y=16

$$4 ^ { y } = 16$$

Solve for y

$$y=2$$

Steps Using Definition of Logarithm

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

$$4^{y}=16$$

Take the logarithm of both sides of the equation.

$$\log(4^{y})=\log(16)$$

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

$$y\log(4)=\log(16)$$

Divide both sides by \log(4).

$$y=\frac{\log(16)}{\log(4)}$$

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

$$y=\log_{4}\left(16\right)$$

Solve for y (complex solution)

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

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