# I have a hard time understanding why ln

I have a hard time understanding why $\mathrm{ln}e=1$
Can someone explain to me why the natural logarithm of e is exactly equal to the first nonzero but positive integer?
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Bruno Dixon
It depends on how you define the natural logarithm; but, let's do it this way:
By definition, $\mathrm{ln}\left(x\right)$ is the unique number $y$ such that ${e}^{y}=x$. In other words, the natural logarithm $g\left(x\right)=\mathrm{ln}\left(x\right)$ is the inverse function for the exponential function $f\left(x\right)={e}^{x}$.
So, $\mathrm{ln}\left(e\right)=1$ because ${e}^{1}=e$
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vasorasy8
that is the definition of $\mathrm{ln}$ (logarithm in base e):
if you take ${\mathrm{log}}_{2}$ (logarithm in base 2) then ${\mathrm{log}}_{2}\left(2\right)=1$ and ${\mathrm{log}}_{2}\left(e\right)=1/\mathrm{ln}\left(2\right)$