Chapter 10: Q. 293 (page 1054)

In the following exercise, solve for x.
$\log_{3} (x^{2} + 3) = \log_{3} 4 x$

Short Answer

Expert verified

The solution of the given expression is $x = 1 x = 3$

Step by step solution

Step 1. Given information.

The given expression is $\log_{3} (x^{2} + 3) = \log_{3} 4 x$

Step 2. Use logarithmic properties

Using one to one property, we get:

$\log_{3} (x^{2} + 3) = \log_{3} 4 x (x^{2} + 3) = 4 x x^{2} - 4 x + 3 = 0$

Step 3. Solve for x.

Solving the equation, we get:

$x^{2} - 4 x + 3 = 0 x^{2} - 3 x - x + 3 = 0 x (x - 3) - (x - 3) = 0 [t a k i n g o u t x a s c o m m o n] (x - 1) (x - 3) = 0 [t a k i n g o u t (x - 3) a s c o m m o n]$

So,

$x = 1$ or

$x = 3$

Step 4. Check the value

Substituting $x = 3$ in the given expression, we get:

$\log_{3} (x^{2} + 3) = \log_{3} 4 x \log_{3} (3^{2} + 3) = \log_{3} 4 \cdot 3 \log_{3} (9 + 3) = \log_{3} 12 \log_{3} 12 = = \log_{3} 12$

This is true

Substituting $x = 1$ in the given expression, we get:

$\log_{3} (x^{2} + 3) = \log_{3} 4 x \log_{3} (1^{2} + 3) = \log_{3} 4 \cdot 1 \log_{3} (4) = \log_{3} 4$

This is true.

Thus, $x = 3 x = 1$ is the solution of the given function.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercise, solve for x.
$\log_{3} (x^{2} + 3) = \log_{3} 4 x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Probability and Statistics

Calculus

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, solve for x.log3x2+3=log34x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Probability and Statistics

Calculus

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, solve for x.
$\log_{3} (x^{2} + 3) = \log_{3} 4 x$