(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi everyone,

I'm trying to proove that for x real, ln(1+x)<=x

2. Relevant equations

3. The attempt at a solution

I know that I can solve this problem by introducing f:=x->ln(1+x)-x and studying f, but I'd like to use x->ln(1+x)'s concavity so I tried to find lambda, x and y in :

ln(1+(lambda)*x+(1-lambda)*y)>=(lambda)*ln(1+x)+(1-lambda)*ln(1+y)...

Any help is welcome...

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# Homework Help: Trying to prove that for x real, ln(1+x)<=x

**Physics Forums | Science Articles, Homework Help, Discussion**