The [[LOG]] math function returns the natural logarithm of a specified numerical value.


{{PageSyntax}}
: {{Parameter|logarithm!}} = [[LOG]]({{Parameter|value}})


{{PageDescription}}
* {{Parameter|value}} MUST be greater than 0. [[ERROR Codes|"Illegal function call" error]] occurs if negative or zero values are used.
* The natural logarithm is the logarithm to the base '''e = 2.718282''' (approximately).
* The natural logarithm of ''a'' is defined as the integral from 1 to ''a'' of dx/x.
* Returns are default [[SINGLE]] precision unless the value parameter uses [[DOUBLE]] precision.


{{PageExamples}}
''Example 1:'' [[FUNCTION]] to find the base ten logarithm of a numerical value.
{{CodeStart}}
 FUNCTION Log10#(value AS DOUBLE) {{Cl|STATIC}}
   Log10# = LOG(value) / LOG(10.#) 
 END FUNCTION '' ''
{{CodeEnd}}

:''Explanation:'' The natural logarithm of the value is divided by the base 10 logarithm. The LOG of ten is designated as a DOUBLE precision return by using # after the Log10 value. The return tells you the number of times 10 goes into a value.


''Example 2:'' A binary FUNCTION to convert [[INTEGER]] values using LOG to find the number of digits the return will be.
{{CodeStart}} '' ''
FUNCTION BIN$ (n&amp;)
  IF n&amp; &lt; 0 THEN EXIT FUNCTION            'positive numbers only! negative error!
  FOR p% = 0 TO INT({{Cl|LOG}}(n&amp; + .1) / {{Cl|LOG}}(2))     ' added +.1 to get 0 to work
    IF n&amp; {{Cl|AND}} 2 ^ p% THEN s$ = "1" + s$ ELSE s$ = "0" + s$  'find bits on
  NEXT p%
  IF s$ = "" THEN BIN$ = "&amp;B0" ELSE BIN$ = "&amp;B" + s$       'check for zero return '' ''
END FUNCTION

{{CodeEnd}}
: ''Explanation:'' The LOG of a '''positive''' [[INTEGER]] value is divided by the LOG of 2 to determine the number of binary digits that will be returned. The FOR loop compares the value with the exponents of two and determines if a bit is ON or OFF as "1" or "0". 


{{PageSeeAlso}}
*[[EXP]], [[&amp;B]] (binary number)
*[[Mathematical Operations#Derived Mathematical Functions|Derived Trigonometric Functions]]


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