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Apr 11, 2015 at 1:00 comment added Vesselin Dimitrov The slightly different notation $\log^{[n]}{X}$, which avoids clearly the conflict with derivatives, was my immediate reaction to the title of this question.
Apr 10, 2015 at 14:01 comment added M.G. True. However, if it comes to the $n$th derivative of $\log$, the context is usually such that it's more preferable to use differential operator notation instead, or the simple explicit expression for it.
Apr 10, 2015 at 13:48 comment added Benoît Kloeckner There is room for confusion for the $n$th derivative of the $\log$ function, though.
Apr 10, 2015 at 13:03 history answered M.G. CC BY-SA 3.0