I seek a function $f(x)$ such that $f(f(x)) = \log(x) \forall x > 0$ .
If possible, $f$ should be monotonic and $\log(x) < f(x) < x, \forall x > 0$
How would I go about this? Does such a function exist?
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Do you mean base-10 logarithm or natural logarithm? – bluestool Jun 13 '19 at 13:27
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@bluestool Any really, the base would just put a multiplicative constant in front. I tend to think in terms of natural logs. – Gabi Jun 13 '19 at 13:29