CPM Homework Help : PC3 Problem 5-35

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5-35.

Solve each of the following equations for $x$ . Give exact answers using fractions, not decimals.

$8^{(x+3)}=32$
Step 1(a):
$(2^3)^{x+3}=2^5$
Step 2(a):
$2^{3x+9}=2^5$
Step 3(a):
$3x+9=5$

$27^{2x}=\left(\frac{1}{9}\right)^{(x-1)}$
Hint (b):
Convert the $\left(\frac{1}{9}\right)$ to $\left(3^{-2}\right)$ .

$\log_3(x)=4$
Hint (c):
Review your work from problem 5-25.
Step (c):
$3^4=x$

$\log_x(64)=3$
Step (d):
$x^3=64$

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