Solve 2^3-2z=1/32

$$2 ^ { 3 - 2 z } = \frac { 1 } { 32 }$$

Solve for z

$$z=4$$

Steps Using Definition of Logarithm

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

$$2^{-2z+3}=\frac{1}{32}$$

Take the logarithm of both sides of the equation.

$$\log(2^{-2z+3})=\log(\frac{1}{32})$$

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

$$\left(-2z+3\right)\log(2)=\log(\frac{1}{32})$$

Divide both sides by \log(2).

$$-2z+3=\frac{\log(\frac{1}{32})}{\log(2)}$$

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

$$-2z+3=\log_{2}\left(\frac{1}{32}\right)$$

Subtract 3 from both sides of the equation.

$$-2z=-5-3$$

Divide both sides by -2.

$$z=-\frac{8}{-2}$$