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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 198 (page 1069)

In the following exercises,solve each logarithmic equation.
$\log_{3} (4 x - 3) = 2$

Short Answer

Expert verified

The solution is $x = 3$ .

Step by step solution

01

Step 1.Given information

Consider the logarithmic equation $\log_{3} (4 x - 3) = 2$ .

The logarithmic from $y = \log_{a} x$ is equivalent to exponential form $x = a^{y}$

02

Step 2.Solve the given logarithmic equation.

Comparing $\log_{3} (4 x - 3) = 2$ with the standard form $y = \log_{a} x$ , you have $y = 2, a = 3, x = 4 x - 3$ .

Convert logarithmic equation in the exponential equation as shown below.

$x = a^{y} 4 x - 3 = 3^{2} 4 x - 3 = 9$

So, the equation is $4 x - 3 = 9$ .

Now solve the equation as

$4 x - 3 + 3 = 9 + 3 [a d d 3] 4 x = 12 [d i v i d e b y 4] x = 3$

So, the solution is $x = 3$

03

Step 3.Check

To check the solution,replace a by 3 in original equation.

$\log_{3} (4 路 3 - 3) = 2 [x = 3] \log_{3} 9 = 2 9 = 3^{2} 9 = 9 [t r u e]$

Therefore, the solution is $x = 3$

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Most popular questions from this chapter

In the following exercise, factor using substitution.

${(x 鈭� 3)}^{2} 鈭� 5 (x 鈭� 3) 鈭� 36$

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$鈸� \frac{y^{43}}{y^{37}} 鈸� \frac{10^{15}}{10^{7}} 鈸� \frac{m^{7}}{m^{15}} 鈸� \frac{9^{8}}{9^{19}}$

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