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

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 $x = a^{y}$

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 $x = 3$

Step 3.Check

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

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

Therefore, the solution is $x = 3$

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

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve the given logarithmic equation.

Step 3.Check

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In the following exercises,solve each logarithmic equation.log3(4x-3)=2

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve the given logarithmic equation.

Step 3.Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Applied Mathematics

Logic and Functions

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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