How to Solve This Logarithmic Problem?

[phy_]

show how

 

[Dick]

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

 

[Mark44]

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. 10^{log a} = a as long as a > 0.

 

[phy_]

Thank-you so much.