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

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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.
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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!
 
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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.
 

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