KermMartian at 19:17, 24 February 2016

2016-02-24T19:17:18Z

← Older revision		Revision as of 19:17, 24 February 2016
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	Using either the [[TI-BASIC:Ln\|Ln(]] or the log( command, logarithms of any base can be calculated, using the identity:		Using either the [[TI-BASIC:Ln\|Ln(]] or the log( command, logarithms of any base can be calculated, using the identity:
	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}}		\log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	So, to take the base B log of a number X, you could use either of the following equivalent ways:		So, to take the base B log of a number X, you could use either of the following equivalent ways:
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	* [[TI-BASIC:Ten_Exponent\|10^(]]		* [[TI-BASIC:Ten_Exponent\|10^(]]
	* [[TI-BASIC:Ln\|Ln(]]		* [[TI-BASIC:Ln\|Ln(]]
	* [[TI-BASIC:Logbase\|logBASE(]][[Category:TI-BASIC]]		* [[TI-BASIC:Logbase\|logBASE(]]
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:12:53Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=LOG.GIF
|summary=Computes the (principal branch of the) base 10 logarithm.
|syntax=log(''value'')
|location=Press the LOG key to paste log(.
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

The log( command computes the base 10 logarithm of a value -- the exponent to which 10 must be raised, to get that value. This makes it the inverse of the [[TI-BASIC:Ten_Exponent|10^(]] command.

log( is a real number for all positive real values. For negative numbers, log( is an imaginary number (so taking log( of a negative number will cause [[TI-BASIC:Errors#nonrealans|ERR:NONREAL ANS]] to be thrown in [[TI-BASIC:Real_Mode|Real]] mode), and of course it's a complex number for complex values. log( is not defined at 0, even if you're in a complex mode.

= Advanced Uses =

Using either the [[TI-BASIC:Ln|Ln(]] or the log( command, logarithms of any base can be calculated, using the identity:
[[TI-BASIC:Math|Math]]
\log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}}
[[TI-BASIC:/math|/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.

The base 10 logarithm specifically can be used to calculate the number of digits a whole number has:

:1+int(log(N))

This will return the number of digits N has, if N is a whole number. If N is a decimal, it will ignore the decimal digits of N.

= Error Conditions =

* '''[[TI-BASIC:Errors#domain|ERR:DOMAIN]]''' when calculating log(0).
* '''[[TI-BASIC:Errors#nonrealans|ERR:NONREAL ANS]]''' if taking log( of a negative number in [[TI-BASIC:Real_Mode|Real]] mode.

= Related Commands =

* [[TI-BASIC:Ten_Exponent|10^(]]
* [[TI-BASIC:Ln|Ln(]]
* [[TI-BASIC:Logbase|logBASE(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Log - Revision history

KermMartian at 19:17, 24 February 2016

Maintenance script: Initial automated import