# 11: Summary

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.

## Learning Outcomes

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.