Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

e and ln

e constant and natural log is inverse of others.

Last edited by Zeeshan 01 (2018-06-22 15:15:30)

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: e and ln

e is maybe the most important constant in mathematics. It is a number and its value is approximately

2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427

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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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: e and ln

ln(x) is the natural log.

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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.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: e and ln

yes and ln how we use it

To expand on bobbym's explanation, ln(e) = 1.
ln(ab) = ln(a) + ln(b)
The derivative of ln(x) is 1/x.
Natural logarithms play a large role in complex numbers, and you will see why.

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: e and ln

To show that you will have to know a bit about the Taylor series for e^x.

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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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: e and ln

Mathematics is just not fun ;it is funny.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: e and ln

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: e and ln

e is maybe the most important constant in mathematics. It is a number and its value is approximately

Last edited by thickhead (2016-07-28 21:46:24)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: e and ln

hi Zeeshan 01

A long time ago someone posted an integration problem requiring a proof.  Along the way I 'proved' a number of properties of e and ln(x).  You might find it useful for this topic.

http://www.mathisfunforum.com/viewtopic.php?id=19468

Bob

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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

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: e and ln

e is maybe the most important constant in mathematics. It is a number and its value is approximately

actually not enough digits

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: e and ln

Hi;

actually not enough digits

How many would you like? There was an interesting article in the early days of computing by Wozniak where he used his algorithm to compute 500 digits of e. Of course, this was before there were any CAS so he cleverly got his small 8 bit, 2 Mhz, Z80 with 16k of ram to do it. A nice exercise with that hardware and it inspired me to become a digit hunter too!

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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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: e and ln

Actually some later digits were not visible in #2 ;so I tried to bring them in.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: e and ln

Problem with latex on this site and the way some programs produce output for latex. Shrinking your browsers  screen will help bring in more digits. I have added a plain test answer to that post.

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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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: e and ln

With my limited knowledge I tried to use\text mode suggested by somebody on the blog and it works well.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}