Prove log(1+x)<x for x>0
my attempt:
I show ex>1+x for x>0 since
ex=1+x+n(n−1)2x2n2+...
so if x>0 then all terms are positive
so ex>1+x for x>0
now given ex>1+x for x>0, can I take log on both sides and show
log(1+x)<x for x>0
or do I have to prove firstly that exp(x)=ex for x>0 then I can take log..
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