Question

求证:log2(π)+log5(π)>2

Answer 1

楼上的错了：搞混了logpi(2)和log2(pi)

正确的做法：

首先log5(pi)/log2(pi)=log5(2)>log8(2)=1/3

其次pi^(4)>3^4>4^3,也就是说pi^(4/3)>4

那么

log2(pi)+log5(pi)=log2(pi)*[1+log5(pi)/log2(pi)]>(4/3)*log2(pi)

根据上面所说的,log2(pi)^(4/3)>log2(4)=2

命题得证.