Log base 2 can be very useful for things that grow by dividing. A great example of this is cell growth.
Edit: The use in my example of that ac straight line on this graph would be that cells are both diving and dieing at constant (can be the same or different from each other) rates. A change in the slope of the line indicates a change in one of those rates which is useful to know. This is also hard to observe directly on a standard base 10 or log base 10 graph
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