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Let 2^x = 3^y = 6^-2 = k
2^x = k
k^(1/x) = 2....(i)
3^y = k
k^(1/y) = 3...(ii)
6^-2 = k
k^(-1/2) = 6...(iii)
(i)*(ii) = (iii)
k^(1/x) * k(1/y) = k^(-1/2)
k^(1/x + 1/y) = k^(-1/2)
1/x + 1/y = -1/2
1/x + 1/y + 1/2 = 0
Hope it helps.
2^x = k
k^(1/x) = 2....(i)
3^y = k
k^(1/y) = 3...(ii)
6^-2 = k
k^(-1/2) = 6...(iii)
(i)*(ii) = (iii)
k^(1/x) * k(1/y) = k^(-1/2)
k^(1/x + 1/y) = k^(-1/2)
1/x + 1/y = -1/2
1/x + 1/y + 1/2 = 0
Hope it helps.
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