Initially there are $2000$ bacteria in a given culture. The number of bacteria $N$ is tripling every hour so $N=2000 \cdot 3^t$, where $t$ is the measurable in hours.
a) How many bacteria are present after $4$ hours?
b) How long is it until there are $1000000$ bacteria?
This is not much of a question because part a) can be solved directly by substituting the number of hours in $N=2000*3^t$ for $t$. As far as b) is concerned, we can do:
$$10^6=2*10^3*3^t$$ So lets solve for $t$, $$\frac{1000}2=500=3^t$$ Thus taking log of both sides, $$\log{500}=t\log3$$ So $$\boxed{t=\frac{\log500}{\log3}=\log_{3}500}$$