Solve 4^y-9=15

$$4 ^ { y - 9 } = 15$$

Solve for y

$$y = \frac{\log_{2} {(15)} + 18}{2} \approx 10.953445298$$

Steps Using Definition of Logarithm

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

$$4^{y-9}=15$$

Take the logarithm of both sides of the equation.

$$\log(4^{y-9})=\log(15)$$

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

$$\left(y-9\right)\log(4)=\log(15)$$

Divide both sides by \log(4).

$$y-9=\frac{\log(15)}{\log(4)}$$

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

$$y-9=\log_{4}\left(15\right)$$

Add 9 to both sides of the equation.

$$y=\frac{\log_{2}\left(15\right)}{2}-\left(-9\right)$$