Lesson 5

So far, you have seen the product and quotient laws of logarithms. There is a third law that is commonly used with logarithms. The next activity explores this rule.

Try This 2

1.  Complete a table like the following:
   
   

   log 2 = log 21 =	1 × log 2 =
   log 4 = log 22 =	2 × log 2 =
   log 8 = log 23 =	3 × log 2 =
   log 16 = log 24 =	4 × log 2 =

2. 1. What pattern do you notice from the table?
   2. Use your rule to predict an alternate way of writing log 54.
   3. Use your rule to predict an alternate way of writing 6 log 2.
3. Does your rule work for other bases, such as log4? Explain.

Save your responses in your course folder.

Share 2

With a partner or group, describe any patterns you see between your rule from Try This 2 and the exponent law (bm)n = bm × n.

If required, save a summary of your discussion in your course folder.