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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 335 (page 1055)

In the following exercises, solve each equation.
$7 \log_{3} (x) = \log_{3} (128)$ .

Short Answer

Expert verified

The solution is $x = 2$ .

Step by step solution

01

Step 1. Given equation is,

$7 \log_{3} (x) = \log_{3} (128) .$

The objective is, we need to find the solution for the given equation.

The power property is given by,

$p \log_{a} (M) = \log_{a} (M^{p})$ .

The one to one property is, if $\log_{a} (M) = \log_{(a)} (N)$ , then $M = N$ .

02

Step 2. Apply the power property in the given equation.

$\log_{3} (x^{7}) = \log_{3} (128)$ .

Now use the one to one property in the obtained equation.

$x^{7} = 128$ .

Now simplify it.

$x^{7} = {(2)}^{7} x = 2$

03

Step 3 Let us check the answer.

Substitute $x = 2$ in the given equation.

$7 \log_{3} (2) = \log_{3} (128) \log_{3} (2^{7}) = \log_{3} (128) \log_{3} (128) = \log_{3} (128)$

which is true.

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