Solve -2^x=-32

$$- 2 ^ { x } = - 32$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

Divide both sides by -1.

$$2^{x}=\frac{-32}{-1}$$

Fraction \frac{-32}{-1} can be simplified to 32 by removing the negative sign from both the numerator and the denominator.

$$2^{x}=32$$

Take the logarithm of both sides of the equation.

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

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

$$x\log(2)=\log(32)$$

Divide both sides by \log(2).

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

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

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

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+5$$

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