$log[]

The function $log[] calculates the natural logarithm (denoted as ln), which is the logarithm in base e (≈ 2.71828).

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

Logarithm of 1:

$log[1]
→ 0

Logarithm of e (approx.):

$log[2.718281828]
→ ~1

Logarithm of a large number:

$log[1000]
→ 6.907755...

Logarithm of a fraction:

$log[0.5]
→ -0.693147...

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).