Question Number 126529 by Study last updated on 21/Dec/20
Commented by Olaf last updated on 22/Dec/20
![Why x^(1/(lnx)) is not e^(ln[x^(1/(lnx)) ]) = e^((1/(lnx))lnx) = e sir ? Why the result is not e.x+C ?](Q126568.png)
$$\mathrm{Why}\:{x}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}} \:\mathrm{is}\:\mathrm{not}\:{e}^{\mathrm{ln}\left[{x}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}} \right]} \:=\:{e}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}\mathrm{ln}{x}} \:=\:{e}\:\mathrm{sir}\:? \\ $$$$\mathrm{Why}\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{not}\:{e}.{x}+\mathrm{C}\:? \\ $$