# Difference between revisions of "LOG"

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− | The | + | 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 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. | + | * 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. | * Returns are default [[SINGLE]] precision unless the value parameter uses [[DOUBLE]] precision. | ||

− | ''Example:'' [[FUNCTION]] to find the base ten logarithm | + | {{PageExamples}} |

− | + | ''Example 1:'' [[FUNCTION]] to find the base ten logarithm of a numerical value. | |

− | + | {{CodeStart}} | |

− | + | {{Cl|FUNCTION}} Log10#(value {{Cl|AS}} {{Cl|DOUBLE}}) {{Cl|STATIC}} | |

− | + | Log10# = {{Cl|LOG}}(value) / LOG(10.#) | |

− | + | {{Cl|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 10 value. | + | :''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}} '' '' | ||

+ | {{Cl|FUNCTION}} BIN$ (n&) | ||

+ | {{Cl|IF}} n& < 0 {{Cl|THEN}} {{Cl|EXIT FUNCTION}} 'positive numbers only! negative error! | ||

+ | {{Cl|FOR}} p% = 0 {{Cl|TO}} {{Cl|INT}}({{Cl|LOG}}(n& + .1) / {{Cl|LOG}}(2)) 'added +.1 to get 0 to work | ||

+ | {{Cl|IF}} n& {{Cl|AND}} 2 ^ p% {{Cl|THEN}} s$ = "1" + s$ {{Cl|ELSE}} s$ = "0" + s$ 'find bits on | ||

+ | {{Cl|NEXT}} p% | ||

+ | {{Cl|IF}} s$ = "" {{Cl|THEN}} BIN$ = "&B0" {{Cl|ELSE}} BIN$ = "&B" + s$ 'check for zero return '' '' | ||

+ | {{Cl|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]], [[&B]] (binary number) | ||

− | |||

− | + | {{PageNavigation}} |

## Latest revision as of 14:52, 5 March 2021

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

## Syntax

*logarithm!*= LOG(*value*)

## Description

*value*MUST be greater than 0. "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.

## Examples

*Example 1:* FUNCTION to find the base ten logarithm of a numerical value.

FUNCTION Log10#(value AS DOUBLE) STATIC
Log10# = LOG(value) / LOG(10.#)
END FUNCTION * *

*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.

* *
FUNCTION BIN$ (n&)
IF n& < 0 THEN EXIT FUNCTION 'positive numbers only! negative error!
FOR p% = 0 TO INT(LOG(n& + .1) / LOG(2)) 'added +.1 to get 0 to work
IF n& 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

*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".

## See also

*Navigation:*