Solve 73=2^2x+3

$$73 = 2 ^ { 2 x + 3 }$$

Solve for x

$$x = \frac{\log_{2} {(73)} - 3}{2} \approx 1.594912279$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$2^{2x+3}=73$$

Take the logarithm of both sides of the equation.

$$\log(2^{2x+3})=\log(73)$$

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

$$\left(2x+3\right)\log(2)=\log(73)$$

Divide both sides by \log(2).

$$2x+3=\frac{\log(73)}{\log(2)}$$

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

$$2x+3=\log_{2}\left(73\right)$$

Subtract 3 from both sides of the equation.

$$2x=\log_{2}\left(73\right)-3$$

Divide both sides by 2.

$$x=\frac{\log_{2}\left(73\right)-3}{2}$$