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.
Using either the ln( or the log( command, logarithms of any base can be calculated, using the identity:(1)
So, to take the base B log of a number X, you could use either of the following equivalent ways:
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:
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.
- ERR:DOMAIN when calculating log(0).
- ERR:NONREAL ANS if taking log( of a negative number in Real mode.