Solve 2^x+5=32

$$2 ^ { x + 5 } = 32$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

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

$$2^{x+5}=32$$

Take the logarithm of both sides of the equation.

$$\log(2^{x+5})=\log(32)$$

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

$$\left(x+5\right)\log(2)=\log(32)$$

Divide both sides by \log(2).

$$x+5=\frac{\log(32)}{\log(2)}$$

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

$$x+5=\log_{2}\left(32\right)$$

Subtract 5 from both sides of the equation.

$$x=5-5$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}$$

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