Question

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

Answer 1

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`