Growth rate of logarithmic function? Just curious about the growth rate of the logarithmic function: Does there exist a real number n such that lim_(x ->oo) ((ln(x))^(n))/(x) diverges (does not converge to 0)? Thanks in advance!

Amira Serrano

Amira Serrano

Answered question

2022-10-12

Growth rate of logarithmic function?
Just curious about the growth rate of the logarithmic function:
Does there exist a real number n such that l i m x ( l n ( x ) ) n x diverges (does not converge to 0)?
Thanks in advance!

Answer & Explanation

getrdone07tl

getrdone07tl

Beginner2022-10-13Added 23 answers

Answer is an emphatic no.
To see this, let y = ln ( x ). Then, as x , y
and ln ( x ) n x = y n e y which goes to 0 as y goes to . (This can be seen easily using the L'Hospital's rule, if you like.)

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