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Question
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(c) whether f(xy) = f(x) : f(y) holds
Solution
Given:
f : R+ → R
and f (x) = logex .............(i)
(c) f (xy) = loge(xy) {From(i)}
= logex + logey [Since logemn = loge m + logen]
= f (x) + f (y)
Thus, f (xy) = f (x) + f (y)
Hence, it is clear that f (xy) = f (x) + f (y) holds.
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