Since most calculators only have base 10 and natural base e on them, logs that have different bases to these are hard to calculate. This theorem allows us to change any log’s base to a base we can calculate easily. It states that:
So say I want to calculate what 
is. There is no log
button on the calculator that has a base of 2. But there is one with a base of
10. Using the above theorem:
We want to change to a base that we can use on our calculator, such as 10, so:
We can now rewrite it as follows:
The right hand side of this we can enter on our
calculators, to get an answer of about 4.09. Since 17 is just a bit more than
16, and 
,
this answer seems to make sense.