Solve 2^x+7=21

$$2 ^ { x + 7 } = 21$$

Solve for x

$$x=\log_{2}\left(21\right)-7\approx -2.607682577$$

Steps Using Definition of Logarithm

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

$$2^{x+7}=21$$

Take the logarithm of both sides of the equation.

$$\log(2^{x+7})=\log(21)$$

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

$$\left(x+7\right)\log(2)=\log(21)$$

Divide both sides by \log(2).

$$x+7=\frac{\log(21)}{\log(2)}$$

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

$$x+7=\log_{2}\left(21\right)$$

Subtract 7 from both sides of the equation.

$$x=\log_{2}\left(21\right)-7$$