By turning multiplication into addition, logarithms make computation simpler, and allow us to work with very large or very small numbers.
Logarithms for multiplication
The original purpose of logarithms was to convert multiplication into addition (and division into subtraction).
Logarithms for precision
Storing and computing with very large or small numbers presents difficulties with precision, but logarithms can be used to avoid such problems.
Simple worked examples
A demonstration of logarithms in action should help our intuitions at this stage.
Definition of logarithms
Now we have an intuitive understanding, we can state the formal definition of logarithms.
Relationships
From that formal definition, we can state the relationships that enable us to convert multiplication into addition, amongst other things.
How to compute logarithms
Calculating the logarithm of a number is quite hard, so we use pre-calculated look-up tables.
