Logarithm examples

Introductory material for understanding logarithms

1. Logarithm Examples by Marian Fine-Kennedy

2. Let’s look at log 5 This is read “log base 5” Log 5 means what exponent of 5 do I need? For example, log 5 5 means what exponent of 5 do I need to get 5 ? It is read “ log base 5 of 5”

3. The answer is 1 , since 5 1 = 5 . Therefore, log 5 5 = 1 “ log base 5 of 5 is 1” Remember, log is a fancy way to ask for an exponent

4. Continuing with log 5 , “log base 5” log 5 25 means what exponent of 5 do I need to get 2 5 ? The answer is 2 , since 5 2 = 25 . Therefore, log 5 25 = 2 “ log base 5 of 25 is 2”

5. Here are several examples with log base 5 log 5 5 = 1 “ log base 5 of 5 is 1” since 5 1 = 5 log 5 25 = 2 “ log base 5 of 25 is 2 ” since 5 2 = 25 log 5 125 = 3 “ log base 5 of 125 is 3” since 5 3 = 1 25 log 5 625 = 4 “ log base 5 of 625 is 4” since 5 4 = 625 Remember, the answer to a logarithm is an exponent

6. Here are several examples with log base 2 log 2 2 = 1 “ log base 2 of 2 is 1” since 2 1 = 2 log 2 4 = 2 “ log base 2 of 4 is 2 ” since 2 2 = 4 log 2 8 = 3 “ log base 2 of 8 is 3” since 2 3 = 8 log 2 16 = 4 “ log base 2 of 16 is 4” since 2 4 = 16

7. Here are several examples with log base 2 continued… log 2 32 = 5 “ log base 2 of 16 is 5” since 2 5 = 32 log 2 64 = 6 “ log base 2 of 16 is 6” since 2 6 = 64 log 2 128 = 7 “ log base 2 of 8 is 7” since 2 7 = 128 log 2 256 = 8 “ log base 2 of 16 is 8” since 2 8 = 256

8. Practice set 1 of 4 Now try these. See if you can fill these in. Attempt these before you click on the next slide to see the answers. You will learn more by attempting them first. log 3 3 = ___ “ log base 3 of 3 is ___ ” since ______ log 3 9 = ___ “ log base 3 of 9 is ___ ” since ______ log 3 27 = ___ “ log base 3 of 27 is ___ ” since ______ log 3 81 = ___ “ log base 3 of 81 is ___ ” since ______

9. Practice set 1 of 4 answers log 3 3 = 1 “ log base 3 of 3 is 1” since 3 1 = 3 log 3 9 = 2 “ log base 3 of 9 is 2 ” since 3 2 = 9 log 3 27 = 3 “ log base 3 of 27 is 3” since 3 3 = 27 log 3 81 = 4 “ log base 3 of 81 is 4” since 3 4 = 81

10. Practice set 2 of 4 Now try these. See if you can fill these in. Attempt these before you click on the next slide to see the answers. You will learn more by attempting them first. log 4 4 = ___ “ log base 4 of 4 is ___ ” since ______ log 4 16 = ___ “ log base 4 of 16 is ___ ” since ______ log 4 64 = ___ “ log base 4 of 64 is ___ ” since ______ log 4 256 = ___ “ log base 4 of 256 is ___ ” since ______

11. Practice set 2 of 4 answers log 4 4 = 1 “ log base 4 of 4 is 1” since 4 1 = 4 log 4 16 = 2 “ log base 4 of 16 is 2 ” since 4 2 = 16 log 4 64 = 3 “ log base 4 of 64 is 3” since 4 3 = 64 log 4 256 = 4 “ log base 4 of 256 is 4” since 4 4 = 256

12. Practice set 3 of 4. Again, see if you can fill these in. Attempt these before you click on the next slide to see the answers. You will learn more by attempting them first. log 6 36 = ___ “ log base _ of _ is ___ ” since ______ log 7 7 = ___ “ log base _ of _ is ___ ” since ______ log 9 81 = ___ “ log base _ of _ is ___ ” since ______ log 10 100 = ___ “ log base _ of _ is ___ ” since ______ log 6 6 = ___ “ log base _ of _ is ___ ” since ______

13. Practice set 3 of 4 answers log 6 36 = 2 “ log base 6 of 36 is 2” since 6 2 = 36 log 7 7 = 1 “ log base 7 of 7 is 1” since 7 1 = 7 log 9 81 = 2 “ log base 9 of 81 is 2” since 9 2 = 81 log 10 100 = 2 “log base 10 of 100 is 2” since 10 2 = 100 log 6 6 = 1 “ log base 6 of 6 is 1” since 6 1 = 6

14. Ok here is your last set to try. Practice set 4 of 4 Again, see if you can fill these in. Attempt these before you click on the next slide to see the answers. You will learn more by attempting them first. log 10 1000 = ___ “ _________________” since ______ log 7 49 = ___ “ _________________” since ______ log 10 10 = ___ “ _________________” since ______ log 8 64 = ___ “ _________________” since ______ log 9 9 = ___ “ _________________” since ______

15. Practice set 4 of 4 answers log 10 1000 = 3 “ log base 10 of 1000 is 3” since 10 3 = 1000 log 7 49 = 2 “ log base 7 of 49 is 2” since 7 2 = 49 log 10 10 = 1 “ log base 10 of 10 is 1” since 10 1 = 10 log 8 64 = 2 “ log base 8 of 64 is 2” since 8 2 = 64 log 9 9 = 1 “ log base 9 of 9 is 1” since 9 1 = 9

16. How did you do? If you did not get the answers, please email me, post to the help forum, email a classmate, or try going through this week’/s materials again. By practicing and repeating the information, you will get it! If you did well, please wait a few days and review the material again to help put the material in your long-term memory.

17. How did you do? Either way, please repeat the information again on at least 2 different days besides today. That will help solidify it for you. Why? Logarithms can be confusing at first, so I want you to get comfortable and familiar with them.

18. How did you do? Make sure you understand why the answer is what it is. When you go back and repeat the slide show, try covering up parts of the examples and see if you can figure out the missing parts. Great job for completing the slide show!