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

Lorelei Stanton

Lorelei Stanton

Answered question

2022-03-26

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

Answer & Explanation

paganizaxpo3

paganizaxpo3

Beginner2022-03-27Added 8 answers

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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?