Logs make it easier to compare measurements that vary by many orders of magnitude.
Positive logs mean big numbers bigger than one.
Negative logs mean small numbers between zero and one.
Logs are the same as the exponent you would need to put on a “10” in order to get your original measurement: in other words, The Log is the Power. Mathematically we write:
if x= 10y then y = log x
Going UP BY ONE on a log scale is always the same as multiplying by 10. Going DOWN BY ONE on a log scale is always the same as dividing by 10.
Given the log you can recover the original measurement by raising 10 to the log (or “10^___ =” on Google). This is also known as the “antilog”.
The pH scale is based on the NEGATIVE log of the concentration of H+ ions.
The Richter scale is based on the log of the amplitude of the wave from an earthquake measured by a seismograph.
After completing this module you should be able to:
- Work with very large and very small numbers by converting between log and linear scales, using logarithms (to the base 10) and anti-logarithms.
- Use the log scale of hydrogen ion concentration (pH) to determine the acidity of a solution.
- Determine the hydrogen ion concentration of a solution from its pH.
If you want a printer-friendly version of this module, you can find it here in a PDF document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.