Question

Prove that (log x/ log 2) + 1 <= 2 log x for all sufficiently large x.

Answer 1

let lhs=(logx/log2)+1=k
=>logx+log2=klog2
=>logx=(k-1)log2
=>2logx=(k-1)2log2>k for all k>1 i.e. for sufficiently large x
=>2log2>(logx/log2)+1