CPM Homework Help : PC Problem 6-148

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6-148.

Solve the following equations for $k$ .

$5 · 3^{(x + 2)} = k · 3^{x}$
Step 1(a):
Divide both sides by $3^{x}$ and both sides by $5$ .
$\frac{3^{(x+2)}}{3^{x}}=\frac{k}{5}$
Step 2 (a):
Rewrite the exponents with one base.
$3^{(x+2)-x}=\frac{k}{5}$
Step 3(a):
Simplify.
$9=\frac{k}{5}$
Answer (a):
$k = 45$

$6 · 2^{(x+k)} = 24 · 2^{x}$
Hint (b):
Follow the same thinking process as in (a).

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