| Property | Value |
|---|---|
| Hex Value | $BE |
| Categories | |
| Localizations |
|
ln(
Overview
Returns the natural logarithm of a real or complex number, expression, or list.
Availability: Token available everywhere.
Syntax
ln(value)
Arguments
| Name | Type | Optional |
|---|---|---|
| value |
Location
ln
Description
The ln( command computes the natural logarithm of a value — the exponent to which the constant e must be raised, to get that value. This makes it the inverse of the e^( command.
ln( is a real number for all positive real values. For negative numbers, ln( is an imaginary number (so taking ln( of a negative number will cause ERR:NONREAL ANS to be thrown in Real mode), and of course it's a complex number for complex values. ln( is not defined at 0, even if you're in a complex mode.
Advanced Uses
Using either the ln( or the log( command, logarithms of any base can be calculated, using the identity:
(1) \(\begin{align} \log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}} \end{align}\)
So, to take the base B log of a number X, you could use either of the following equivalent ways:
:log(X)/log(B)
:ln(X)/ln(B)
This is the exponent to which B must be raised, to get X.
Error Conditions
- ERR:DOMAIN when calculating ln(0).
- ERR:NONREAL ANS if taking ln( of a negative number in Real mode.
Related Commands
Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Timothy Foster.
History
| Calculator | OS Version | Description |
|---|---|---|
| TI-82 | 1.0 | ln added |
| TI-83 | 0.01013 | Renamed ln to ln( |