Question

Demonstrează că 1-ln2>o....

Answer 1

 

$\displaystyle\bf\\\text{Trebuie sa demonstram ca }~~~1-\ln2>0\\\\\text{Folosim urmatoarea relatie:}\\\\\ln x<0~~daca~~0<x<1\\\ln x=0~~daca~~x=1\\\ln x>0~~daca~~x>1\\\\Rezolvare:\\Folosim~egalitatea:~\underline{\bf\ln e =1}\\\\1-\ln2=\ln e-\ln2 = \ln\left(\frac{e}{2} \right)\\\\\frac{e}{2}>0~deoarece~e>2\\\\\implies~\ln\left(\frac{e}{2} \right)>0\\\\\boxed{\bf\implies~1-\ln2>0}~cctd$