# How do you solve for x for ln1 - lne = x?

Feb 17, 2015

The result should be: $x = - 1$

Consider that from the definition of logarithm:

${\log}_{a} b = x \implies {a}^{x} = b$

and that ${\log}_{e}$ is $\ln$;

So you get:

$\ln 1 = 0$ because ${e}^{0} = 1$

$\ln e = 1$ because ${e}^{1} = e$

$0 - 1 = x$
$x = - 1$