# TI-BASIC:Log

**Command Summary**

Computes the (principal branch of the) base 10 logarithm.

**Command Syntax**

log(*value*)

**Menu Location**

Press the LOG key to paste log(.

TI-83/84/+/SE

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 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 ERR:NONREAL ANS to be thrown in 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 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.

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

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