TI-BASIC:Ln

From Learn @ Cemetech
Jump to navigationJump to search

LN.GIF

Command Summary

Computes the (principal branch of the) natural logarithm.

Command Syntax

ln(value)

Menu Location

Press the LN key to paste ln(.

Calculator Compatibility

TI-83/84/+/SE

Token Size

1 byte

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: <math> \log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}} </math>

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

Related Commands