The most general (correct) form of this statement is "use the expectimax algorithm". Yeah, it's a bit weird that he's prescribing log as the mapping from dollars to utility.

If log is the correct mapping for you, it actually doesn't matter what base you use. It just comes out as a constant factor on the expected utility.

Sum_d P(d) U(d) = Sum_d P(d) log_b(d) = Sum_d P(d) log(d)/log(b) = (1/log(b)) Sum_d P(d) log(d)