The ln( Command

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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:

(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

• e
• e^(
• log(
• logBASE(

.