* {{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&)
IF n& < 0 THEN EXIT FUNCTION 'positive numbers only! negative error!
FOR p% = 0 TO INT({{Cl|LOG}}(n& + .1) / {{Cl|LOG}}(2)) ' added +.1 to get 0 to work
IF n& {{Cl|AND}} 2 ^ p% THEN s$ = "1" + s$ ELSE s$ = "0" + s$ 'find bits on
NEXT p%
IF s$ = "" THEN BIN$ = "&B0" ELSE BIN$ = "&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".