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Calc Question

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user098123
Posts: 6072 - Karma: 18
Im trying to use L'Hopitals rule to determine which function, f(x) or g(x) is increasing at a faster rate. The section I'm on has problems that are all a natural log on the top and some form of a root of X on the bottom. On this problem, for example:

the limit as x approaches infinity of
ln^5(x)
--------
(x)^1/3

My question is what exactly is the ln^5(x) mean? Can it be rewritten as ln(x)^5 and then bring the 5 in front of the natural log so its 5ln(x) by the rules of natural logs? or does it mean something else?

All help is greatly appreciated.
Feb 6 2007 12:12AM
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user098123
Posts: 6072 - Karma: 18
buuump...anyone know?
Feb 6 2007 12:26AM
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freezed
Posts: 12973 - Karma: 500
it sure seems like you could just pull the 5 down to make it 5ln(x), then the derivative of that is just 5/x
Feb 6 2007 12:28AM
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user098123
Posts: 6072 - Karma: 18
thats what i was hoping, the thing that threw me off was that the superscript power of 5 is written in between the ln and the X where as it is usually ln(x)^5, maybe its just the preference of the author or somethin? not entirely sure.
Feb 6 2007 12:31AM
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freezed
Posts: 12973 - Karma: 500
thats just how its written...same with trig functions. ln^5(x) is exactly the same as (ln x)^5
Feb 6 2007 12:35AM
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4-Front
Posts: 5306 - Karma: 199
i dont know anything bout calc yet but im sure that lnx^5 is equal to 5lnx. you should review your log laws or just search google. oh and x>0 and the base is (e).
Feb 6 2007 12:49AM
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Itsbackfliptime
Posts: 18901 - Karma: 75
its the same as 5 lnx.
Feb 6 2007 11:29AM
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Chubby.Chaser
Posts: 2926 - Karma: 15
it's not 5ln(x), it's (ln(x))^5

use the chain rule and you will have to apply l'hopital's rule 5 times to elimate the ln terms

the answer is zero
Feb 6 2007 3:21PM
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49566738265
Posts: 0 - Karma: 7,704
nope
Feb 6 2007 3:44PM
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49566738265
Posts: 0 - Karma: 7,704
this guy is correct, its just like how:

(cosx)^2 is the same as cos^2x
Feb 6 2007 3:46PM
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user098123
Posts: 6072 - Karma: 18
No, it is 5ln(x). Seriously go study some laws of natural logs, or any logarithmic function as well as e^(x). If you have any one of those functions to an exponent it can be brought in front of the function, so that ln(x)^5 = 5ln(x) and then you dont have to use l'hopitals 5 times, that would suck.
Feb 6 2007 6:04PM
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guava
Posts: 271 - Karma: 10
calc 2 was the absolute worst class i have taken in college thus fur, waaaaay worse than chem. sorry just had to share my distain for calc, good luck with ur hw man i'd help but ive forgotten all my calc knowledge already
Feb 6 2007 6:12PM
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wAy2sTeEzY4u
Posts: 5449 - Karma: 20
math threads make me feel stupid....its not one of my strong points at all...im basically in retard classes for math.
Feb 6 2007 6:15PM
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