CPM Homework Help : PC3 Problem 13-80

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Home > PC3 > Chapter 13 > Lesson 13.2.2 > Problem 13-80

13-80.

Solve for $x$ in each of the following equations.

$3^{x} = 7$
Hint (a):
Take the log of both sides.

$9^{2x}=27^{x-2}$
Step (b):
$(3^2)^{2x}=(3^3)^{x-2}$

$\log_2\left(\log_9\left(\log_3\left(x\right)\right)\right)=-1$
Step 1(c):
$2^{-1}=\log_9\left(\log_3\left(x\right)\right)$
$\log_9(\log_{3}(x))=\frac{1}{2}$
Step 2(c):
$9^{1/2}=\log_3(x)$
$\log_{3}(x) = 3$

$\left(x-3\right)\left(\ln\left(x\right)-2\right)=0$
Step (d):
$x-3=0$ or $\ln\left(x\right)-2=0$

Compute without a calculator

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