Solve 2^4x-13=1/32

$$2 ^ { 4 x - 13 } = \frac { 1 } { 32 }$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$2^{4x-13}=\frac{1}{32}$$

Take the logarithm of both sides of the equation.

$$\log(2^{4x-13})=\log(\frac{1}{32})$$

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

$$\left(4x-13\right)\log(2)=\log(\frac{1}{32})$$

Divide both sides by \log(2).

$$4x-13=\frac{\log(\frac{1}{32})}{\log(2)}$$

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

$$4x-13=\log_{2}\left(\frac{1}{32}\right)$$

Add 13 to both sides of the equation.

$$4x=-5-\left(-13\right)$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Solve for x (complex solution)

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

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