LN

Return the natural logarithm (base e) of a positive number. The inverse of EXP.

Syntax

LN(number)

Argument	Required	Description
`number`	Required	A positive number.

Examples

Every example below was executed against VisiGrid engine 0.54.0 — not transcribed from another vendor's documentation. Reproduce any of them with vgrid calc.

Formula	Result	Notes
`=LN(1)`	`0`
`=LN(EXP(2))`	`2`	LN undoes EXP.
`=LN(10)`	`2.30`
`=LN(B2/A2)`	`0.80`	The log return from 9 to 20.
`=LN(0)`	`#NUM!`	Zero and negative numbers have no logarithm.

LN, LOG and LOG10

Three functions, three bases. LN is base e. LOG10 is base 10. LOG defaults to base 10 and takes any base as a second argument. Programmers should note that log() in most languages is the natural log — here that is LN, and LOG is base 10.

Doubling time

How many years something growing at 7% takes to double:

=LN(2)/LN(1.07)  → 10.24

The same pattern answers any “how long until it reaches X” question — divide the log of the target multiple by the log of the growth factor.

Log returns

LN(end/start) is the continuously compounded return between two prices. Unlike simple percentage returns, log returns over consecutive periods add up, so a SUM of them is the return over the whole span.

Excel compatibility

Matches Excel, including #NUM! for zero and negative input.