### Home > CCA2 > Chapter Ch2 > Lesson 2.1.2 > Problem2-18

2-18.

Solve for z in each equation below. Homework Help ✎

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.

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

2. $4^{2z/3}=8^{(z+2)}$

Follow the steps in part (a). Notice that both 4 and 8 can be rewritten as powers of 2.

3. $3^z=81^2$

Follow the steps in part (a).

4. $5^{(z+1)/3}=25^{1/z}$

$25=5^{2}$

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

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

$z = -3, 2$
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