# TI-BASIC:Ln

**Command Summary**

Computes the (principal branch of the) natural logarithm.

**Command Syntax**

ln(*value*)

**Menu Location**

Press the LN key to paste ln(.

TI-83/84/+/SE

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

**ERR:DOMAIN**when calculating ln(0).**ERR:NONREAL ANS**if taking ln( of a negative number in Real mode.