Solve 2^n+2=2

$$2 ^ { n + 2 } = 2$$

Solve for n

$$n=-1$$

Steps Using Definition of Logarithm

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

$$2^{n+2}=2$$

Take the logarithm of both sides of the equation.

$$\log(2^{n+2})=\log(2)$$

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

$$\left(n+2\right)\log(2)=\log(2)$$

Divide both sides by \log(2).

$$n+2=\frac{\log(2)}{\log(2)}$$

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

$$n+2=\log_{2}\left(2\right)$$

Subtract 2 from both sides of the equation.

$$n=1-2$$