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Find a/b when 2*log(a - b) = log(a) + log(b).

 Oct 20, 2021
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Find a/b when 2*log(a - b) = log(a) + log(b).

 

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\(2\cdot log(a - b) = log(a) + log(b). \\ (a-b)^2=ab\\ a^2-2ab+b^2=ab\ |\ -ab\\ a^2-3ab+b^2=0\ |\ +\frac{a}{b} \\ a^2-3ab+b^2+\frac{a}{b}=\frac{a}{b} \)

\(\dfrac{a}{b}=\dfrac{a^2b-3a+b^3+a}{b}\\ \color{blue}\dfrac{a}{b}=\dfrac{a^2b-2a+b^3}{b}\\\)

laugh  !

 Oct 20, 2021
edited by asinus  Oct 20, 2021

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