Difference between revisions of "Manuals/calci/LN"

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<div style="font-size:30px">'''LN(n)'''</div><br/>
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<div style="font-size:30px">'''LN(Number)'''</div><br/>
*where <math>n</math> is the positive real number.
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*where <math>Number</math> is the any positive real number.
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**LN() returns the natural logarithm of a number.
  
 
==Description==
 
==Description==
 
*This function gives the Natural Logarithm of a number.
 
*This function gives the Natural Logarithm of a number.
 
*<math>LN</math> is the  logarithm in which the base is the irrational number <math>e</math> (<math>e</math>= 2.71828...).
 
*<math>LN</math> is the  logarithm in which the base is the irrational number <math>e</math> (<math>e</math>= 2.71828...).
*For example, <math>ln_10 = loge_10 = \approx 2.30258</math>
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*For example, <math>ln_10 = loge_10 \approx 2.30258</math>
*Also called Napierian logarithm.
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*It was formely also called Hyperbolic logarithm.
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*And also called Napierian logarithm.
 
*The constant <math>e</math> is called Euler's number.
 
*The constant <math>e</math> is called Euler's number.
 
*The Natural Logarithm is denoted by <math>ln(x)</math> or <math>log e(x)</math>.
 
*The Natural Logarithm is denoted by <math>ln(x)</math> or <math>log e(x)</math>.
 
*where <math>x</math> is the Positive real number.
 
*where <math>x</math> is the Positive real number.
*The ln(x) is the inverse function of the exponential function e^ln(x)=x if x>0.
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*The <math>ln(x)</math> is the inverse function of the exponential function <math>e^{ln(x)}=x</math> if <math>x>0</math>.
ln(e^x)=x
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*<math>ln(e^x)=x</math>
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==ZOS==
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*The syntax is to calculate Natural logarithm in ZOS is <math>LN(number)</math>.
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**where <math>number</math> is the any positive real number.
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*For e.g.,LN(20..23)
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{{#ev:youtube|OCirVf3pulA|280|center|Natural Logarithm}}
  
 
==Examples==
 
==Examples==
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*=LN(8.3) = 2.116255515
 
*=LN(8.3) = 2.116255515
 
*=LN(1) = 0
 
*=LN(1) = 0
*=LN(0) = INFINITY
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*=LN(0) = -INFINITY
 
*=LN(-20) = NAN
 
*=LN(-20) = NAN
 
*=LN(exp(5)) = 5
 
*=LN(exp(5)) = 5
 
*=EXP(LN(7)) = 7
 
*=EXP(LN(7)) = 7
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==Related Videos==
 +
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{{#ev:youtube|eavkIcjXchI|280|center|Natural Logarithm}}
  
 
==See Also==
 
==See Also==
 
*[[Manuals/calci/LOG | LOG]]
 
*[[Manuals/calci/LOG | LOG]]
 
*[[Manuals/calci/EXP | EXP]]
 
*[[Manuals/calci/EXP | EXP]]
*[[Manuals/calci/IML  | IML]]
 
  
 
==References==
 
==References==
 
[http://en.wikipedia.org/wiki/Natural_logarithm  Natural Logarithm]
 
[http://en.wikipedia.org/wiki/Natural_logarithm  Natural Logarithm]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 05:52, 8 June 2020

LN(Number)


  • where is the any positive real number.
    • LN() returns the natural logarithm of a number.

Description

  • This function gives the Natural Logarithm of a number.
  • is the logarithm in which the base is the irrational number (= 2.71828...).
  • For example,
  • It was formely also called Hyperbolic logarithm.
  • And also called Napierian logarithm.
  • The constant is called Euler's number.
  • The Natural Logarithm is denoted by or .
  • where is the Positive real number.
  • The is the inverse function of the exponential function if .

ZOS

  • The syntax is to calculate Natural logarithm in ZOS is .
    • where is the any positive real number.
  • For e.g.,LN(20..23)
Natural Logarithm

Examples

  • =LN(15) = 2.708050201
  • =LN(8.3) = 2.116255515
  • =LN(1) = 0
  • =LN(0) = -INFINITY
  • =LN(-20) = NAN
  • =LN(exp(5)) = 5
  • =EXP(LN(7)) = 7

Related Videos

Natural Logarithm

See Also

References

Natural Logarithm