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| − | <div id=" 16SpaceContent" align="left"><div class="ZEditBox" align="justify"> | + | <div style="font-size:30px">'''LN(Number)'''</div><br/> |
| | + | *where <math>Number</math> is the any positive real number. |
| | + | **LN() returns the natural logarithm of a number. |
| | | | |
| − | Syntax
| + | ==Description== |
| | + | *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...). |
| | + | *For example, <math>ln_10 = loge_10 \approx 2.30258</math> |
| | + | *It was formely also called Hyperbolic logarithm. |
| | + | *And also called Napierian logarithm. |
| | + | *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>. |
| | + | *where <math>x</math> is the Positive real number. |
| | + | *The <math>ln(x)</math> is the inverse function of the exponential function <math>e^{ln(x)}=x</math> if <math>x>0</math>. |
| | + | *<math>ln(e^x)=x</math> |
| | | | |
| − | </div></div> | + | ==ZOS== |
| − | ----
| + | *The syntax is to calculate Natural logarithm in ZOS is <math>LN(number)</math>. |
| − | <div id="4SpaceContent" align="left"><div class="ZEditBox" align="justify"> | + | **where <math>number</math> is the any positive real number. |
| | + | *For e.g.,LN(20..23) |
| | + | {{#ev:youtube|OCirVf3pulA|280|center|Natural Logarithm}} |
| | | | |
| − | Remarks
| + | ==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 |
| | | | |
| − | </div></div>
| + | ==Related Videos== |
| − | ----
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| − | <div id="2SpaceContent" align="left"><div class="ZEditBox" align="justify">
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| | | | |
| − | Examples
| + | {{#ev:youtube|eavkIcjXchI|280|center|Natural Logarithm}} |
| | | | |
| − | </div></div>
| + | ==See Also== |
| − | ----
| + | *[[Manuals/calci/LOG | LOG]] |
| − | <div id="8SpaceContent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman">''''''''''''<font size="6"> </font>''' '''''''''</font>'''</div></div>
| + | *[[Manuals/calci/EXP | EXP]] |
| − | ----
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| − | <div id="11SpaceContent" align="left"><div class="ZEditBox mceEditable" align="justify">
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| | | | |
| − | <font size="5">Description</font>
| + | ==References== |
| | + | [http://en.wikipedia.org/wiki/Natural_logarithm Natural Logarithm] |
| | | | |
| − | </div></div>
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| − | ----
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| − | <div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman"> <font size="6">LN</font> </font>'''</div></div>
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| − | ----
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| − | <div id="3SpaceContent" class="zcontent" align="left"><br /><div id="7Space" class="gamizbox" title="7Space"><div id="7SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="7SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="7SpaceRollupContent" align="center"></span></span></div><div id="7SpaceCover"><div id="7SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">
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| − | '''LN'''('''n1''')… where n1 is the positive real number
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| | | | |
| − | </div></div>
| + | *[[Z_API_Functions | List of Main Z Functions]] |
| − | ----
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| − | <div id="13SpaceContent" class="zcontent" align="left"><br /><br /><div id="1Space" class="gamizbox" title="1Space"><div id="1SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="1SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="1SpaceRollupContent" align="center"></span></span></div><div id="1SpaceCover"><div id="1SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="3">
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| − | <font face="Times New Roman">LN is the inverse of the EXP function.</font>
| + | *[[ Z3 | Z3 home ]] |
| − | | |
| − | <font face="Times New Roman"> </font>
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| − | | |
| − | </font></div></div>
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| − | ----
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| − | <div id="14SpaceContent" class="zcontent" align="left"><br /><br /><br /><div id="5Space" class="gamizbox" title="5Space"><div id="5SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="5SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="5SpaceRollupContent" align="center"></span></span></div><div id="5SpaceCover"><div id="5SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">
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| − | | |
| − | LN function gives you the natural logarithm of a number.
| |
| − | | |
| − | </div></div>
| |
| − | ----
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| − | <div id="12SpaceContent" class="zcontent" align="left"><br /><br /><br /><div id="9Space" class="gamizbox" title="9Space"><div id="9SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="9SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="9SpaceRollupContent" align="center"></span></span></div><div id="9SpaceCover"><div id="9SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="3"><font face="Times New Roman">
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| − | | |
| − | Lets see an example in (Column1, Row 1)
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| − | LN (n1)
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| − | LN (C1R1)''''''
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| − | | |
| − | That is LN (35) is 3.56
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| − | | |
| − | </font></font></div></div>
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| − | ----
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| − | <div id="6SpaceContent" class="zcontent" align="left">
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| − | | |
| − | {| id="TABLE3" class="SpreadSheet blue"
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| − | |- class="even"
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| − | | class=" " |
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| − | <div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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| − | | Column1
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| − | | class=" " | Column2
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| − | | class=" " | Column3
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| − | | class=" " | Column4
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| − | |- class="odd"
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| − | | class=" " | Row1
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| − | | class="sshl_f" | 35
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| − | | class="sshl_f" |
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| − | |- class="even"
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| − | | class=" " | Row2
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| − | | class="sshl_f" | 3.5553
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| − | | class="sshl_f" |
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| − | |- class="odd"
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| − | | Row3
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| − | | class="sshl_fSelectTD SelectTD " |
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| − | <div id="6Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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| − | | class="sshl_f" |
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| − | | class="sshl_f" |
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| − | |- class="even"
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| − | | class="sshl_f" |
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| − | |- class="odd"
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| − | | class=" " | Row5
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| − | | class="sshl_f" |
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| − | | class="sshl_f" |
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| − | |- class="even"
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| − | | Row6
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| − | | class="sshl_f" |
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| − | | class="sshl_f" |
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| − | | class="sshl_f" |
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| − | | class="sshl_f" |
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| − | |}
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| − | <div align="left">[[Image:calci1.gif]]</div></div>
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| − | ----
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| − | </div></div></div></div></div></div></div></div></div></div></div></div>
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is the any positive real number.
