Syntax

$log[value]

Parameters

Parameter	Type	Required	Description
value	number	Yes	The number whose logarithm to calculate. Must be > 0.

Behavior

• Returns the natural logarithm of the value as a decimal number (double precision).
• $log[1] → 0 (because e^0 = 1).
• $log[e] → 1 (because e^1 = e).
• For 0 or negative numbers, the behavior is undefined (may return -Infinity, NaN or generate an error).

Examples

Natural Logarithm Calculation

$title[Math: Natural Logarithm]
$description[Logarithm of `1`: **$log[1]**]
$addField[Log of 1000;$log[1000];yes]
$addField[Log of 0.5;$log[0.5];yes]
$color[#5865F2]
$sendMessage[]

Notes

• This is the natural logarithm (base e), not the base 10 logarithm.
• For base 10 logarithm, use inside $calculate[]: $calculate[log10(value)].
• For a logarithm in an arbitrary base, use the change of base formula: log_b(a) = ln(a) / ln(b), which translates to $calculate[log(a) / log(b)].
• The inverse function is exponential: $calculate[exp(value)].
• The precision matches that of a Java double (~15 significant digits).