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48 lines
1.7 KiB
Markdown
48 lines
1.7 KiB
Markdown
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The [LOG](LOG) math function returns the natural logarithm of a specified numerical value.
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## Syntax
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> logarithm! = [LOG](LOG)(value)
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## Description
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* value MUST be greater than 0. [ERROR Codes](ERROR-Codes) occurs if negative or zero values are used.
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* The natural logarithm is the logarithm to the base **e = 2.718282** (approximately).
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* The natural logarithm of *a* is defined as the integral from 1 to *a* of dx/x.
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* Returns are default [SINGLE](SINGLE) precision unless the value parameter uses [DOUBLE](DOUBLE) precision.
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## Example(s)
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[FUNCTION](FUNCTION) to find the base ten logarithm of a numerical value.
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```vb
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FUNCTION Log10#(value AS DOUBLE) STATIC
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Log10# = LOG(value) / LOG(10.#)
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END FUNCTION
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```
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> *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.
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A binary FUNCTION to convert [INTEGER](INTEGER) values using LOG to find the number of digits the return will be.
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```vb
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FUNCTION BIN$ (n&)
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IF n& < 0 THEN EXIT FUNCTION 'positive numbers only! negative error!
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FOR p% = 0 TO INT(LOG(n& + .1) / LOG(2)) ' added +.1 to get 0 to work
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IF n& AND 2 ^ p% THEN s$ = "1" + s$ ELSE s$ = "0" + s$ 'find bits on
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NEXT p%
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IF s$ = "" THEN BIN$ = "&B0" ELSE BIN$ = "&B" + s$ 'check for zero return
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END FUNCTION
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```
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> *Explanation:* The LOG of a **positive** [INTEGER](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".
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## See Also
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*[EXP](EXP), [&B](&B) (binary number)
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