1. Lesson 5

1.10. Explore 6

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

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.

 

Try This 4

 

This is a photo of a pH scale. Some food items are shown on the 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.

  1. What would be the pH of vinegar that has the following concentration of hydrogen ions: [H+] = 0.006 31 mol/L.
  2. Coffee has a pH of 5.4. How many times as acidic as coffee is vinegar?
  3. A lemon-flavoured pop has a pH of 2.8. A cola-flavoured pop is 3 times as acidic as the lemon-flavoured pop. What is the pH of the cola-flavoured pop?

course folder Save your responses in your course folder.

 

tip

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.

 

Using the quotient law of logarithms, you could write the equation
To compare the food products, you must compare the concentration of hydrogen ions, not the pH. Also ask yourself how the quotient law of logarithms could be used.
Use the formula pH = − log [H+].