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

## Syntax

logarithm! = LOG(value)

## Description

- value MUST be greater than 0. ERROR Codes 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.

## Example(s)

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.

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 apositiveINTEGER 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”.