Question

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

Answer 1

答案：
解析：

证明：∵n＞1,且n∈N, ∴logn(n+1)＞0,log(n+1)(n+2)＞0. ∴=log(n+1)(n+2)·log(n+1)n ＜［］2 =［］2 ＜［］2=1. 故logn(n+1)＞log(n+1)(n+2)(n＞1,n∈N).