Definition of a logarithm:
is equivalent to if or and if .
It follows from the definition of a logarithm that: and .
Properties of logarithms:
If or and if and the following properties hold:
Changing the base:
In order to be able to work with a desired base (the log-button of your calculator always uses 10) you need to be able to change an existing base.
From the properties of logarithms you can derive: .
In this way you can determine logarithms with your calculator and/or enter them as a function. Note that modern calculators sometimes allow you to choose the base of the logarithm. You then need to use the American notation , where the base is written in a different position.