Reading and Interpreting Numbers on Logarithmic Axes

Go back

When data is plotted on logarithmic scales, the numbers are typically represented with one of two formats.

  1. The raw numbers themselves are plotted on a logarithmic axis.LOG SCALE -- RAW NUMBERS
  2. The raw numbers are first converted to their log values (exponents of 10) and these are plotted on a linear axis.
    LOG SCALE -- LOGARITHMS

The two scales above cover an identical range of numbers but differ in their utility as illustrated by two representations of the titration curve of acetic acid.


By the first format, the raw numbers themselves are plotted on a log axis with the major intervals of the X-axis (the darker vertical lines in this plot) corresponding to a power of 10, e.g., 10-7, 10-6, etc., as read from left to right!
Acetic Acid Titration vs. [H+]

By the second format, the raw numbers are first converted to their logarithmic values and these are plotted on a linear axis as illustrated below.
Acetic Acid Titration vs. pH

Both graphs represent exactly the same data.  In other words, they are there quantitatively equivalent.  However, the different formats provide easy access to different types of information about the titration. For example:


Go to top
Go back
Duane W. Sears
Revised: September 30, 2010