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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

Hi;

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

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

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

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

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

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

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 )

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

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

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

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

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

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

I know these all formulas!!!

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

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

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

Your 2nd step of implies that confusing me !!!

Because we must balance eq when we add any value we also subtract so ???

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

Why e^(lny)=y

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

ln and e^ are inverse functions

E hat??

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

to the power of e some say exp

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

Exponent? ?

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

Microsoft exel?? How come there

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

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,447

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

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

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 719

Useful tool

M.M.Zeeshan.K

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