Chapter 10: Q. 199 (page 1034)

In the following exercises,solve each logarithmic equation.
$\log_{3} (5 x - 4) = 4$

Short Answer

Expert verified

The solution is $x = 17$ .

Step by step solution

Step 1.Given information

Consider the logarithmic equation $\log_{3} (5 x - 4) = 4$ .

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

Step 2.Solve the given logarithmic equation

Comparing $\log_{3} (5 x - 4) = 4$ with the standard form $y = \log_{a} x$ ,you have $y = 4, a = 3, x = 5 x - 4$

Convert logarithmic equation in exponential equation as shown below

$x = a^{y} 5 x - 4 = 3^{4} 5 x - 4 = 81$

So,the solution is $5 x - 4 = 81$

Now solve the equation as

$5 x - 4 + 4 = 81 + 4 [a d d 4] 5 x = 85 [d i v i d e b y 5] x = 17$

So,the solution is $x = 17$

Step 3.Check

To check the solution,replace a by 17 in original equation

$\log_{3} (5.17 - 4) = 4 [x = 17] \log_{3} 81 = 4 3^{4} = 81 81 = 81 [t r u e]$

Therefore,the solution is $x = 17$

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In the following exercises,solve each logarithmic equation.
$\log_{3} (5 x - 4) = 4$

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(5x-4)=4

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

Discrete Mathematics

Pure Maths

Decision Maths

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises,solve each logarithmic equation.
$\log_{3} (5 x - 4) = 4$