# How do you simplify ln(1/e) ?

Mar 2, 2018

$- 1$

#### Explanation:

Division rule of logarithms states that:

$\ln \left(\frac{x}{y}\right) = \ln \left(x\right) - \ln \left(y\right)$

Here we can substitute:

$\ln \left(\frac{1}{e}\right) = \ln \left(1\right) - \ln \left(e\right)$

1) Anything to the power $0 = 1$

2) $\ln \left(e\right) = 1$, as the base of natural logarithms is always $e$

Here, we can simplify:

$\ln \left(1\right) = 0$
$\ln \left(e\right) = 1$

Thus:

$\ln \left(1\right) - \ln \left(e\right) = 0 - 1$

$= - 1$