How to Solve This Logarithmic Problem?

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Homework Help Overview

The discussion revolves around a logarithmic equation involving variables x and y, specifically focusing on manipulating logarithmic expressions and exploring their properties.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss multiplying both sides of the equation by 2 and rewriting logarithmic expressions. There is an exploration of the implications of equal logarithms and the potential steps to take next.

Discussion Status

Participants are actively engaging with the problem, with some offering transformations of the equation and questioning the next steps. There is a sense of collaboration as they seek to clarify the reasoning behind their manipulations.

Contextual Notes

Some participants express a need for further guidance on how to proceed after the initial transformations, indicating that the problem may have multiple interpretations or approaches.

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Multiply both sides by 2, 2*log((x-y)/3)=log(x)+log(y). Now what? Show us what you try.
 
log((x - y)/3) = 1/2(log x + log y)
==> log((x - y)/3) = 1/2(log xy)
==> log((x - y)/3) = log (xy)1/2

Now, if the logs of two numbers are equal, then the two numbers must be equal. (Equivalently you could exponentiate each side of the equation; that is, make each side the exponent on 10. 10log a = a as long as a > 0.
 
Thank-you so much.
 

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