We know that the population in 20 years ( ) is triple the starting one ( ):
It follows that
and
.
Now set up equation for doubling in unknown time:
and get from that
Exponentials to all bases and logarithms to all bases are interchangable. I prefer to avoid "e" in favor of an obvious base.
Saying that a population take "T" years to triple is the same as saying it is given by since "t/T" is the number of times it triples. So asking for the number of years to double is asking form t such that . Divide both sides by C and take the logarithm (to any convenient base) of both sides: (t/T)log(3)= log(2), t= T (log(2)/log(3)).
Here, T= 20 so the time to double is 20 (log(2)/log(3)).