Logarithm is a function of mathematics which is used to calculate inverse function of exponents. The asymptotically smallest function will be the one that has smallest or no exponents. The exponent function is calculated in reverse when log is applied. The function with highest exponents will be largest asymptotically.
He already had 100 into the account so we add that, 25x is derived from the fact that x=the amount of months and 25 is the amount per a month he saves.
