Question

求证:log_n(n+1)＞log_(n+1)(n+2)(n＞1,n∈N).

Answer 1

证明：∵n＞1,且n∈N,

∴log_n(n+1)＞0,log_(n+1)(n+2)＞0.

∴=log_(n+1)(n+2)·log_(n+1)n

＜［］²

=［］²

＜［］²=1.

故log_n(n+1)＞log_(n+1)(n+2)(n＞1,n∈N).