# What is ln(e^x)?

Nov 11, 2015

It is exactly $x$.
You are looking for a number that is the exponent of the base of $\ln$ which gives us the integrand, ${e}^{x}$;
the base of $\ln$ is $e$;
the number you need to be the exponent of this base to get ${e}^{x}$ is.....exactly $x$!!!
$\ln \left({e}^{x}\right) = {\log}_{e} \left({e}^{x}\right) = x$