Chapter 11: Q. 52 (page 774)

Solve the system. Use any method you wish.
$\{\begin{cases} \log_{x} (2 y) = 3 \\ \log_{x} (4 y) = 2 \end{cases}$

Short Answer

Expert verified

The solution of system of equations are $(\frac{1}{2}, \frac{1}{16})$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\{\begin{cases} \log_{x} (2 y) = 3 \\ \log_{x} (4 y) = 2 \end{cases}$

Using logarithmic rules,

$2 y = x^{3} . . . . . . (i) 4 y = x^{2} . . . . . . (i i)$

Rewrite equation (i),

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

Step 2. Substitute the value of y in equation (ii).

Substituting the value of y in equation (ii),

$4 (\frac{x^{3}}{2}) = x^{2} 2 x = 1 x = \frac{1}{2}$

Substituting the value of x in equation (ii),

$4 y = {(\frac{1}{2})}^{2} y = \frac{1}{4} \times \frac{1}{4} y = \frac{1}{16}$

Therefore, the solution sets are $(\frac{1}{2}, \frac{1}{16})$ .

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.

Solve the system. Use any method you wish.
$\{\begin{cases} \log_{x} (2 y) = 3 \\ \log_{x} (4 y) = 2 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the value of y in equation (ii).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the system. Use any method you wish.logx2y=3logx4y=2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the value of y in equation (ii).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the system. Use any method you wish.
$\{\begin{cases} \log_{x} (2 y) = 3 \\ \log_{x} (4 y) = 2 \end{cases}$