What is the point of logarithms? How are they used? Why do you need logarithms?
In what situations do you use them?

In the geometric view of real numbers there are two basic forms of "movements", namely (a) shifts: each point $x\in{\mathbb R}$ is shifted a given amount $a$ to the right and (b) scalings: all distances between points are enlarged by the same factor $b>0$. In some instances (e.g. sizes of adults) the first notion is appropriate for comparison of different sizes, in other instances (e.g. distances between various celestial objects) the second notion. The logarithm provides a natural means to transform one view into the other: The sum of two shifts corresponds to the composition of two scalings.
