From Förberedande kurs i matematik 1

The notation ln is used for the logarithm with the natural base \displaystyle e = 2\textrm{.}7182818\ldots\,, and we therefore have that \displaystyle \ln e = 1\,, which together with the logarithm law, \displaystyle b\lg a=\lg a^b, gives that

\displaystyle \ln e^3 + \ln e^2 = 3\cdot\ln e + 2\cdot \ln e = 3\cdot 1 + 2\cdot 1 = 5\,\textrm{.}