Activities

Logarithms - change of base

How long does $1 take to grow to $1000000 if it doubles every hour?

Solve  2n = 1000000.




Logs to base 2 are not available on the calculator!

Instead take logs of both sides to base 10 and rearrange.

It follows that:




This is an example of the general change of base rule:



The change of base rule can be used to rearrange the compound interest formula to solve for n:

How could the same result be obtained without using the change of base rule?