### Home > INT3 > Chapter 2 > Lesson 2.2.1 > Problem2-42

2-42.

Solve for $z$ in each equation.

1. $2^z=2^3$

1. $4^z=8$

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

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

1. $3^z=81^2$

Follow the steps in part (b).

1. $5^{(z+1)/3}=25^{1/z}$

$25=5^{2}$

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

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

$z=−3,2$