Solve 2^y-5=15

$$2 ^ { y - 5 } = 15$$

Solve for y

$$y=\log_{2}\left(15\right)+5\approx 8.906890596$$

Steps Using Definition of Logarithm

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

$$2^{y-5}=15$$

Take the logarithm of both sides of the equation.

$$\log(2^{y-5})=\log(15)$$

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

$$\left(y-5\right)\log(2)=\log(15)$$

Divide both sides by \log(2).

$$y-5=\frac{\log(15)}{\log(2)}$$

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

$$y-5=\log_{2}\left(15\right)$$

Add 5 to both sides of the equation.

$$y=\log_{2}\left(15\right)-\left(-5\right)$$

Solve for y (complex solution)

$$y=\frac{i\times 2\pi n_{1}}{\ln(2)}+\log_{2}\left(15\right)+5$$

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