$sum _(a,b,c) (1/ (1+ log _a bc)) = 1$ Prove it?

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Answer 1 · 2018-03-21T09:21:16

Since $log_a b = log b/log a$ , we have

$1/(1+log_a bc) = 1/(1+(log (bc))/log a) = log a/(log a+log (bc)) = log a/log(abc)$

Thus, the sum is

$log a/log(abc) + log b/log(abc) + log c/log(abc) = (log a +log b+ log c)/log(abc) = log(abc)/log(abc) = 1$

sum _(a,b,c) (1/ (1+ log _a bc)) = 1 sum _(a,b,c) (1/ (1+ log _a bc)) = 1 Prove it?