1. Lesson 3

1.4. Explore 3

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

In Try This 2 you may have noticed that the logarithm is equal to the exponent from the exponential form. The relationship between the logarithmic and exponential forms are summarized in the illustration shown.

 

This is a diagram that shows the logarithmic and exponential forms and the positions of the base and the exponent. 1

 

tip
Logarithms with base 10 are often used and are called common logarithms. An example of a common logarithm is when you evaluated log 1000. There is no base written, but it is assumed that the base is 10. So, log 1000 is the same as log10 1000.

View Evaluating Logarithms for more examples of how to evaluate logarithms. Compare this method of evaluation with your table from Try This 2.

 

 

This is a play button that opens Evaluating Logarithms.

 

Here is another explanation of logarithms: “Introduction to Logarithms.” However, if you feel confident with logarithms, skip the video and move on to Self-Check 1.

 

 

This is a play button that opens “Introduction to Logarithms.”

Source: Khan Academy
(cc icon BY-NC-SA 3.0)


 

Self-Check 1

 

textbook

  1. Complete questions 2.b., 2.d., 3.b., and 4 on page 380 of the textbook. Answer
  2. Determine the inverse of the function y = 3x.
    1. Write the inverse and leave the function in exponential form. Answer
    2. Isolate y by writing the function in logarithmic form. Answer
  3. Express the following equations in exponential form; then solve for p.
    1. logc 1 = p Answer
    2. logc c = p Answer
    3. logc cx = p Answer
1 graphic:  Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.