Solve 4^y=15

$$4 ^ { y } = 15$$

Solve for y

$$y = \frac{\log_{2} {(15)}}{2} \approx 1.953445298$$

Steps Using Definition of Logarithm

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

$$4^{y}=15$$

Take the logarithm of both sides of the equation.

$$\log(4^{y})=\log(15)$$

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

$$y\log(4)=\log(15)$$

Divide both sides by \log(4).

$$y=\frac{\log(15)}{\log(4)}$$

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

$$y=\log_{4}\left(15\right)$$

Solve for y (complex solution)

$$y=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(15\right)}{2}$$

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