Rewrite both sides of the equation so they have the same base. Now the exponents must be equal. Write an equation and solve for $z$.

$2^{2z}=2^{3}$

Follow the steps in part (b).

$25=5^{2}$

$\frac{z+1}{3}=\frac{2}{z}$

Get all the terms on one side of the equation, factor, and use the Zero Product Property.

$z=−3,2$