# How do you evaluate ln(e) - 3 ln(1/e) - ln(e^3)?

Mar 29, 2016

If you know that "ln" is the natural logarithm, you might know that is a logarithm in base "e".

#### Explanation:

$\ln \left(e\right) - 3 \ln \left(\frac{1}{e}\right) - \ln \left({e}^{3}\right)$ = $1 - 3 \left(- 1\right) - 3$ = 1.

Remember, the answer to a log is the power (exponent).
$\ln \left(e\right) = 1$ since e is to the first power.
$3 \ln \left(\frac{1}{e}\right) = 3 \left(- 1\right)$ since e is to the -1 power.
and $\ln \left({e}^{3}\right) = 3$ since e is to the third power.