Home > PC > Chapter 6 > Lesson 6.4.1 > Problem6-148

6-148.

Solve the following equations for $k$

1. $5 · 3^{(x + 2)} = k · 3^{x}$

Divide both sides by $3^{x}$ and both sides by $5$.

$\frac{3^{(x+2)}}{3^{x}}=\frac{k}{5}$

Rewrite the exponents with one base.

$3^{(x+2)-x}=\frac{k}{5}$

Simplify.

$9=\frac{k}{5}$

$k = 45$

1. $6 · 2^{(x+k)} = 24 · 2^{x}$

Follow the same thinking process as in (a).