Table of Contents

• Prequiz...
• Everything you always wanted to know about logs (but were too bored to ask)
• 1: When size matters
• 2: There must be a better way!
• 3: Special cases
• 4: The log is the power!
• 5: What about messy numbers?
• 6: And SMALL messy numbers?
• 7: Your turn with messy numbers
• 8: Antilogs
• So what are they good for?
• 9: Measuring earthquakes
• 10: Measuring acidity
• 11: Differences in acidity
• Review
• 12: Summary

Summary

Logs make it easier to compare measurements that vary by many orders of magnitude.

Positive logs mean big numbers – bigger than one.
To find the approximate log, simply count the number of digits AFTER the first digit.

Negative logs mean small numbers – between zero and one.
To find the approximate log, count the number of zeros after the decimal point and  the first non-zero digit.

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.

Going UP BY ONE on a log scale is the same as multiplying by 10. Going DOWN BY ONE on a log scale is the same as dividing by 10. (But this is reversed for pH because pH is the negative log of [H⁺])

You can recover the original measurement by raising 10 to the log ( or "10^___ =" on Google).

The pH scale is based on the NEGATIVE log of concentration of H⁺ ions.

The Richter scale is based on the log of energy released.

You should now 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.

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 Microsoft Word 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.