Solve 2^frac{5{2}-b}=4

$$2 ^ { \frac { 5 } { 2 } - b } = 4$$

Solve for b

$$b=\frac{1}{2}=0.5$$

Steps Using Definition of Logarithm

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

$$2^{-b+\frac{5}{2}}=4$$

Take the logarithm of both sides of the equation.

$$\log(2^{-b+\frac{5}{2}})=\log(4)$$

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

$$\left(-b+\frac{5}{2}\right)\log(2)=\log(4)$$

Divide both sides by \log(2).

$$-b+\frac{5}{2}=\frac{\log(4)}{\log(2)}$$

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

$$-b+\frac{5}{2}=\log_{2}\left(4\right)$$

Subtract \frac{5}{2} from both sides of the equation.

$$-b=2-\frac{5}{2}$$

Divide both sides by -1.

$$b=-\frac{\frac{1}{2}}{-1}$$