Consider the sum of the terms, #ln(1/e)+ln(ab)#
The function #ln# here is defined as a function that for whatever value you enter, you get the supposed number of times you're supposed to multiply the number #e# with itself.
In simple terms, #ln(x)# equals #y#, where #y# is such a number that when #e*e*e*.....*e*e# for #y# times (or in short #e^y#) gives back #x# to us.
Take note of the first term given in the sum. #ln(1/e)#.
#1/e# can be re-written as #e^-1#
So, #ln(1/e)=ln(e^-1)#
Another important identity of #ln# function is that if we have a #y=x^m#, then #ln(y)=ln(x^m)=mlnx# #AAm inRR#
So, #ln(e^-1)=-1*lne# and if you remember what I typed up in the third paragraph, then you'll realize that #lne=1#, so #ln(1/e)=-1#
#ln(ab)# can't be simplified further than it is, so we'll have to keep it that way.
Replacing the term for #ln(1/e)# with what we've got, we come to the conclusion as written in the "answers" part.
