Strange Algebra

Algebra Level 4

Let \(\color {Red}{'S'}\) be the ordered pairs of \(\color{Blue}{(x,y)}\) such that \(\color{Green}{0<x\le 1}\) and \( \color{Purple}{0<y\le 1}\) and \(\color{Brown}{ [\ log _3(\frac{1}{x})\ ]}\)and \(\color{DarkRed}{[ \ log _5(\frac{1}{y}) \ ]}\) are both even.

While plotting a graph between the values of \(\color{DarkRed}{x,y}\) that satisfy the condition the area of the graph comes out to be of the form \(\color{Maroon}{\frac{m}{n}}\) where \(\color{Magenta}{m}\) and \(\color{magenta}{n}\) are co-prime integers.

Then what is the value of \(\color{Green}{m+n ?}\) \[\color{Red}{NOTE}\]

  • \(\color{Magenta}{[ .]}\) represents \(\color{Magenta}{GIF}\)

For eg. - [1.2]=1 , [2.3]=2


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