The general exponential form can be converted to logarithm form as follows
where ln denotes the natural logarithm. In our case, a is equal to 1 and b is the number e, so we get
Therefore, the answer is
[tex]\ln e=1[/tex]
Second way.
We hace the following equation:
[tex]e^1=e[/tex]
By applying natural logarithm in both sides, we have
[tex]\ln (e^1)=\ln e[/tex]
But
[tex]\begin{gathered} \ln e=1 \\ \text{then, we have } \\ \ln (e^1)=1 \end{gathered}[/tex]
By the logarithm property:
[tex]\ln x^y=y\ln x[/tex]
we have that
[tex]1\ln e=1[/tex]
since every number times 1 is the same number,(that is, 1 times lne is lne), we get
[tex]\ln e=1[/tex]
