Solve 2^y+11=27

$$2 ^ { y } + 11 = 27$$

Solve for y

$$y=4$$

Steps Using Definition of Logarithm

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

$$2^{y}+11=27$$

Subtract 11 from both sides of the equation.

$$2^{y}=16$$

Take the logarithm of both sides of the equation.

$$\log(2^{y})=\log(16)$$

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

$$y\log(2)=\log(16)$$

Divide both sides by \log(2).

$$y=\frac{\log(16)}{\log(2)}$$

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

$$y=\log_{2}\left(16\right)$$

Solve for y (complex solution)

$$y=\frac{i\times 2\pi n_{1}}{\ln(2)}+4$$

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