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#1 2017-04-28 19:16:39

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Question

Hi;
Differentiate y=a^x by using ln and e???


MZk

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#2 2017-04-28 19:50:05

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

hi,

If you take logs of both sides (base e) then

Differentiate with respect to x:

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2017-04-28 20:35:02

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

logs of both sides (base e)  why you don't wright lne???


MZk

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#4 2017-04-28 22:03:36

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

are different ways of writing the same thing.  ln was the quickest for me.  (But not as it turned out, as I've had to add this post smile )

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2017-04-28 22:49:45

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

Is it possible y=e^(alnx)???


MZk

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#6 2017-04-28 23:43:00

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

Is it possible y=e^(alnx)???

You can differentiate this:

Replacing the first part by y brings you back to my earlier answer. 

My version is the one that you will find in lists of standard differentials such as:

http://www.math.wustl.edu/~freiwald/131 … etable.pdf

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2017-04-29 00:36:49

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

I know these all formulas!!!


MZk

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#8 2017-04-29 00:37:52

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

I also know the simple method u do on top but confused in notes about y=e^(alnx)???


MZk

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#9 2017-04-29 00:40:44

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

Your 2nd step of implies that confusing me !!!
Because we must balance eq when we add any value we also subtract so ???


MZk

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#10 2017-04-29 00:42:21

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

Why e^(lny)=y


MZk

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#11 2017-04-29 01:09:15

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

We have met this before.  ln and e^ are inverse functions.

If y = e^x then x = ln(y)

So if you raise ln(something) to the power of e, the ln and e cancel out, and you're left with the 'something'  ... in this case just y

It's like doubling one half of something.  Doubling 'undoes' the effect of halving so you get back to where you started.

One way to define a log is to say it has this property.

eg  If y = a^x then we define the log of y (in base a) to be x.

Or you can say, if I have a number y, what power of 'a' will give me y.  This power of 'a 'is called the log of y.

eg.  What power of 10 will give me 1000 ?  Answer 3.  So we say 3 = log(1000) in base 10.

So you can always re-write a power expression as a log expression or the other way round.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2017-04-29 01:49:58

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

ln and e^ are inverse functions
E hat??


MZk

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#13 2017-04-29 01:58:24

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

to the power of e  some say exp

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2017-04-29 02:39:29

Zeeshan 01
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Registered: 2016-07-22
Posts: 648

Re: Question

Exponent? ?


MZk

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#15 2017-04-29 03:57:37

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

Not exactly.  Microsoft Excel uses it to mean:

You will find a lot of helpful maths on this site:

http://www.mathsisfun.com/algebra/expon … ithms.html

When you want a new topic, use the search engine at the top of every page, or the cross-links between pages.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#16 2017-04-29 04:04:34

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 648

Re: Question

Microsoft exel?? How come there

Last edited by Zeeshan 01 (2017-04-29 04:05:06)


MZk

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#17 2017-04-29 06:13:35

bob bundy
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Registered: 2010-06-20
Posts: 8,168

Re: Question

Well it is.  I don't know why you're surprised.  Am I missing something?  If you have that software then give it a try.  If you don't then stop worrying.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#18 2017-04-29 14:58:29

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 648

Re: Question

I used this software when I am 6 days old !!! HEHEHE MICROSOFT all applications


MZk

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#19 2017-04-29 14:59:31

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 648

Re: Question

Useful tool


MZk

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