Question

If $lo{g}_2(x+y)=lo{g}_3(x-y)=\frac{log25}{log0.2}$, find the values of $x$ and $y$.

Answer 1

Given $lo{g}_2(x+y)=lo{g}_3(x-y)=\frac{log25}{log0.2}$

$lo{g}_2(x+y)=lo{g}_3(x-y)=\frac{log{5}^2}{log{5}^{-}1}$

$lo{g}_2(x+y)=lo{g}_3(x-y)=\frac{2\times log5}{-1\times log5}$

$lo{g}_2(x+y)=lo{g}_3(x-y)=-2$

$lo{g}_2(x+y)=-2$ and $lo{g}_3(x-y)=-2$

$x+y=2^{-2}$ -----------(1) and $x-y=3^{-2}$​​​​​​​ ----------(2)

Solving (1) and (2) we get

$x=\frac{13}{72}$ and $y=\frac{5}{72}$