You have practised using the laws of logarithms to simplify expressions. You can also use the laws to help you simplify problems. In Try This 4 you will use what you have learned to solve a problem with a logarithmic scale.
The pH scale is a logarithmic scale that is used to communicate the acidity or alkalinity of a solution. To determine the pH of a solution, the equation used is pH = − log [H+], where [H+] is the concentration of hydrogen ions measured in moles per litre (mol/L). The square brackets around [H+] indicate concentration. Refer to the image to see pH values for some common substances. Also make note of the pH values that describe acidic, neutral, and basic substances.
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Logarithmic scales are useful when you have a very large range of values. In the pH scale, the concentration of hydrogen ions has a very large range between solutions. Many logarithmic scales are base 10, so this means that an increase of 1 on the scale is actually a factor of 10. For example, a pH of 4 is 10 times more acidic than a pH of 5.