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.
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.