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:

_{}

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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.