An Introduction to Logarithms

“Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures”

Log vs Linear Scales- Intuition Where does 6 belong? Dahaene et al,

“Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures”

Why is a log scale useful? Make sense of a broad range of data Large range of inputs can be “mapped” to a limited number of outputs

Ex. human hearing Range of intensities humans must process is enormous ▫Barely audible  permanent damage ▫10 12 change in intensities!

Loudness L = 10 log (I/I o ) (in dB)

Other Applications of Logarithms pH Richter scale

pH Measure of H+ ion concentration ▫Measure of acidity pH = -log [H+]

Richter Scale Measure of magnitude of an earthquake Above 4- “moderate” R = log (I/I o )