Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Ln e ?????

Hi I have a question that :solve the differential eq
First tell what is differential eq  and also method
And other thing
If there is -x how we go to this step -xlne and second step is lne^-x       ln(c.e^-x)

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ln e ?????

Hi;

Like a regular equation is a relationship between variables, a differential equation is a relationship between functions and their derivatives.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Ln e ?????

Ok but how this  If there is -x how we go to this step -xlne and second step is lne^-x       ln(c.e^-x)

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Malik

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Ln e ?????

Ok but how this  If there is -x how we go to this step -xlne and second step is lne^-x       ln(c.e^-x)

That is a property of logarithms. 2log(10) = log(10^2).
Could you please clarify your last step? What is c.e^x????

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The integral of hope is reality.
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He will be sorely missed.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Ln e ?????

And I found that ln e is one in calculator but what is e^ln??? Is it possible

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ln e ?????

e^(ln(1)) = 1

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,432

Website

Re: Ln e ?????

And I found that ln e is one in calculator but what is e^ln??? Is it possible

is the inverse of

. To answer your question,

for any

Last edited by zetafunc (2017-04-01 09:34:24)

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Ln e ?????

e^(ln(1)) = 1 how there is 1 come from ???

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Malik

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,432

Website

Re: Ln e ?????

The answer is above your post.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Ln e ?????

Means???

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Ln e ?????

Here are some pairs of function and inverse function:

y = 2x and y = x/2

y = x^3 and y = x^(1/3)

y - e^x and  y = ln(x)

If you start with x = 1, apply any function, get a number, then apply the inverse function to that, you get back to 1.  That's what an inverse function does.  It takes you back to the number you started with.

Using the function grapher, if you plot y = e^x and also y = ln(x) you will see the two functions are inverses of each other.  Another way to test for inverse functions is to plot them both and draw in the line y=x.  If it is a line of symmetry between the two curves, then they are inverses of each other.

Or you could consider the properties of ln(x).  For any logarithmic function log(1) is always zero.  Now raise e to the power zero.  Any value raised to the power zero is always 1.  So we are back where we started.

Bob

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iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: Ln e ?????

Hi Zeesan 01,

Log is nothing but the the power to which a fixed number (the base) must be raised to produce a given number. 

If

, then

. Now,

. How? Just convert               

into exponential form where you will get,

which is absolutely correct. So similarly, Ln is nothing but log to the base e. So

And for more information on logarithms visit http://www.mathsisfun.com/algebra/index-2.html

Last edited by iamaditya (2017-04-06 23:40:08)

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Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Ln e ?????

Hmm

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Malik