Solve 4^y+4=7

$$4 ^ { y + 4 } = 7$$

Solve for y

$$y=\frac{\log_{2}\left(7\right)-8}{2}\approx -2.596322539$$

Steps Using Definition of Logarithm

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

$$4^{y+4}=7$$

Take the logarithm of both sides of the equation.

$$\log(4^{y+4})=\log(7)$$

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

$$\left(y+4\right)\log(4)=\log(7)$$

Divide both sides by \log(4).

$$y+4=\frac{\log(7)}{\log(4)}$$

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

$$y+4=\log_{4}\left(7\right)$$

Subtract 4 from both sides of the equation.

$$y=\frac{\log_{2}\left(7\right)}{2}-4$$