# What is log_e of e?

Sep 25, 2014

${\log}_{e} e = \ln e = 1$
($\ln$ is a button on you GC, equivalent to ${\log}_{e} e$)

By definition the ${\log}_{a} a = 1$, whatever $a$ is.
(as long as $a \ne 0$ and $a \ne 1$)

What ${\log}_{a} x$ means is:
What exponent do I use on $a$ to get $x$?

Example: ${\log}_{10} 1000 = 3$ because ${10}^{3} = 1000$

So ${\log}_{10} 10 = 1$ because ${10}^{1} = 10$
And this goes for any $a$ in ${\log}_{a} a$ because ${a}^{1} = a$

Mar 24, 2015

$\ln \left(e\right)$ is the same thing as ${\log}_{e} \left(e\right)$
Because ${e}^{1} = e , {\log}_{e} \left(e\right) = 1$