How to Prove log[(x-y)/3] = 1/2(logx+logy) Equals x^2+y^2=11xy?

  • Thread starter Thread starter phy_
  • Start date Start date
  • Tags Tags
    Log
AI Thread Summary
To prove that log[(x-y)/3] = 1/2(logx + logy) is equivalent to x^2 + y^2 = 11xy, one can start by multiplying both sides of the logarithmic equation by 2. Then, applying properties of logarithms and exponentials will help in simplifying the equation. It is essential to reference logarithmic properties from textbooks or online resources for clarity. Showing each step in the solution process is crucial for understanding. The question has been successfully resolved.
phy_
Messages
16
Reaction score
0
show how log [(x-y)/3]=1/2(logx+logy) is equal to xsquared+ysquared=11xy

does anyone know how to solve this.
i have tried all kinds of ways though none of them seem to work.
any help would be very much appreciated!
 
Physics news on Phys.org
What if you multiply both sides by 2? After that, use properties of logarithms and exponentials to solve the problem. Study properties of logarithms in your textbook, or even on-line. List relevant equations, and show your work.
 
Thank-you. Question has been solved.
 

Similar threads

Proving Log Relationship: x2 + y2 = 11xy and log [(x-y)/3] = 0.5(logx + logy)
Replies
2
Views
2K
How to graph by hand: y=log((x/(x+2))
Replies
3
Views
1K
Prove that ## g(x)=f(x)\log {x}-\int_{2}^{x}t^{-1}f(t)dt ##.
Replies
7
Views
1K
Proving Irregularity of {(x, y, z) within R^3 : x^2 + y^2 - z^2 = 0}
Replies
14
Views
3K
(log√125 + log √27 - √8)/ log 15 - log 2 = 3/2
Replies
16
Views
5K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
Replies
10
Views
2K
Limiting Logarithm: x→0+ log(x-1+√(x^2+1))-logx
Replies
12
Views
2K
Express ##x^3+y^3## in terms of ##m## and ##n##
Replies
17
Views
3K
POTW Inequality of Positive Real Numbers: Proving (1-1/x^2)(1-1/y^2)≥9 with x+y≤1
Replies
12
Views
3K
Solving MATLAB Meshgrid: A Beginner's Guide
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top