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#1 2005-09-16 19:15:04

Núria
Guest

limit of a logarithm

I would like to know, if the limit of a logarithmic funcation, lim(log(x)), when x --> infinity, is log(lim(x)) when x--> infinty, due to the logarithmic function behavior.

Thanks!
Núria

#2 2005-09-16 23:59:21

núria
Guest

Re: limit of a logarithm

Núria wrote:

I would like to know, if the limit of a logarithmic funcation, lim(log(ax/bx+c)), when x --> infinity, is log(lim(ax/bx+c)) when x--> infinty, due to the logarithmic function behavior.
Thanks!
Núria

#3 2005-09-17 03:56:10

Flowers4Carlos
Full Member

Offline

Re: limit of a logarithm

hi there Nuu.... uu... ria!!!

just for reference reasons, here is the graph of logx :

as we can see, logx will go to ∞ when x gets larger and larger.  but ∞ is not a number and consequently we cannot evaluate log(∞).  however, if we know what happens to x as it approaches ∞, we can easily compute the limit of logt.  here is how:

lim(x->∞ ) logx
as x -> ∞, we know t = x -> (∞) = ∞
lim(t->∞ )logt = ∞

hope this helps!!!