Solve 4^y+5=30

$$4 ^ { y + 5 } = 30$$

Solve for y

$$y=\frac{\log_{2}\left(30\right)-10}{2}\approx -2.546554702$$

Steps Using Definition of Logarithm

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

$$4^{y+5}=30$$

Take the logarithm of both sides of the equation.

$$\log(4^{y+5})=\log(30)$$

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

$$\left(y+5\right)\log(4)=\log(30)$$

Divide both sides by \log(4).

$$y+5=\frac{\log(30)}{\log(4)}$$

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

$$y+5=\log_{4}\left(30\right)$$

Subtract 5 from both sides of the equation.

$$y=\frac{\log_{2}\left(30\right)}{2}-5$$