Question

which is smaller : 2 or ( log2 to the base e-1 + log e-1 to the base 2).... pls answer me soon !

Answer 1

Use AM-GM inequality:
$\dfrac{\log_{e-1}2+\log_{2}(e-1)}{2}\ge\sqrt{\log_{e-1}2\cdot\log_{2}(e-1)}\\\Rightarrow \log_{e-1}2+\log_{2}(e-1)\ge2\\But \log_{e-1}2+\log_{2}(e-1)\ne2\\\Rightarrow \log_{e-1}2+\log_{2}(e-1)>2$