Lesson 5

Discover

 

So far, you have seen that logarithms and exponents are closely related.

 

 

 

 

There are rules that can be used to combine powers with the same base. The next activity explores a related set of rules for logarithms.

 

Try This 1

1. Complete a table like the following:
   
   

   log 100 + log 1000	= 2 + 3	= 5	= log ____
   log 10 + log 100	=	=	= log ____
   log 10 000 + log 0.01	=	=	= log ____

2.  
   1. Explain any patterns you see in the table.
   2. Use your pattern to predict a rule for simplifying log M + log N.
3. Check that your pattern works with numbers that are not powers of 10 by completing a table like the following using a calculator:
   
   

   log 12 + log 3 =	log 36 =
   log 5 + log 7 =	log ____ =
   log 4 + log 9 =	log ____ =

4. Predict a rule for simplifying log M − log N.

5. Complete a table like the following using a calculator to test your rule:
   
   

   log 18 − log 6 =	log ____ =
   log 8 − log 2 =	log ____ =
   log 10 − log 5 =	log ____ =

Save your responses in your course folder.

 

Share 1

 

With a partner or group, describe any patterns you see between the addition and subtraction rules for logarithms you developed in Try This 1 and the following exponent laws:

 

(bm)(bn) = bm+n

 

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