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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. 436 (page 1065)

In the following exercises, solve for x.
$\ln (3 x - 2) = \ln (x + 4) + \ln 2$

Short Answer

Expert verified

The value of x for the equation $\ln (3 x - 2) = \ln (x + 4) + \ln 2$ is $10$

Step by step solution

01

Step 1. Given data

The given Logarithmic Equation is $\ln (3 x - 2) = \ln (x + 4) + \ln 2$

02

Step 2. Apply product property of the logarithm

Use product property of the logarithm

$\ln (3 x - 2) = \ln (x + 4) + \ln 2 \ln (3 x - 2) = \ln ((x + 4) 2) \ln (3 x - 2) = \ln (2 x + 8)$

03

Step 3. Apply one to one property of the logarithm

Use one to one property of the logarithm

$\ln (3 x - 2) = \ln (2 x + 8) 3 x - 2 = 2 x + 8 3 x - 2 x = 8 + 2 x = 10$

04

Step 4. verification

Substitute $10$ for x in the equation

$\ln (3 x - 2) = \ln (2 x + 8) \ln (3 (10) - 2) \overset{?}{=} \ln (2 (10) + 8) \ln (30 - 2) \overset{?}{=} \ln (20 + 8) \ln (28) = \ln (28)$

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Most popular questions from this chapter

In the following exercises, solve each equation.

$\frac{e^{x^{2}}}{e^{3}} = e^{2 x}$

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In the following exercises, solve each equation.

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$x^{\frac{1}{3}} = \sqrt[3]{6}$ .

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