Another way to do this is to recognize that "half" life means that the amount is multiplied by 1/2 every 3.6 days- In T days, there are T/3.6 periods of 3.6 days each which means the initial amount is multiplied by 1/2 T/3.6 times:

. You want to solve

or, dividing both sides by 20,

. To solve that take the logarithm of both sides (it doesn't matter whether you take the natural logarithm or common logarithm)

so [tex]T= 3.6\frac{log(7/20)}{log(1/2)}= 3.6\frac{log(20)- log(7)}{log(2)}, exactly what Soroban got.

The moral is that all logarithms and all exponentials are equivalent. It doesn't matter what base you use so use whatever is simplest.