How can I show that \lim_{x\rightarrow\infty}\frac{\log(x+1)}{\log x}=1?

redupticslaz

redupticslaz

Answered question

2022-04-25

How can I show that limxlog(x+1)logx=1?

Answer & Explanation

bailaretzy33

bailaretzy33

Beginner2022-04-26Added 15 answers

You could use l'Hospital's rule:
limxlog(x+1)log(x)=limx1x+11x=limx1x+1x=limx11+1x
=11+limx1x=11+0=1

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