If ( 3 x ) log 3 = ( 4 y ) log 4 , 4 log x = 3 log y then x + y x - y =

Question

If ${(3 x)}^{\log 3} = {(4 y)}^{\log 4}$ , $4^{\log x} = 3^{\log y}$ then $\frac{x + y}{x - y} =$ __________.

Smart Achievers · Accepted Answer

(7)

$Taking log on both sides, we get$

$\log 3 (\log 3 + \log x) = \log 4 (\log 4 + \log y)$

$\log x \cdot \log 4 = \log y \cdot \log 3$

$\Rightarrow$ $\log x = - \log 3,$ $\log y = - \log 4$

$\Rightarrow$ $x = \frac{1}{3},$ $y = \frac{1}{4} \Rightarrow \frac{x + y}{x - y} = 7$

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