This document provides examples of logarithms with different bases. It explains that a logarithm asks what exponent is needed for the base to equal the input number. Several practice sets with explanations are provided to help the reader learn how to determine the exponent from the logarithm. The document emphasizes practicing and reviewing the material on multiple occasions to fully understand logarithms.

1. Logarithm Examples
by Marian Fine-Kennedy

2. Let’s look at log5
This is read “log base 5”
Log5 means what exponent of 5 do I need?
For example, log55 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 51 = 5.
Therefore, log55 = 1
“log base 5 of 5 is 1”
Remember, log is a fancy way to ask for an exponent

4. Continuing with log5, “log base 5”
log525 means what exponent of 5 do I need to get 25?
The answer is 2, since 52 = 25.
Therefore, log525 = 2
“log base 5 of 25 is 2”

5. Here are several examples with log base 5
log55 = 1
“log base 5 of 5 is 1”
since 51 = 5
log525 = 2
“log base 5 of 25 is 2 ”
since 52 = 25
log5125 = 3 “log base 5 of 125 is 3” since 53 = 125
log5625 = 4 “log base 5 of 625 is 4” since 54 = 625
Remember, the answer to a logarithm is an exponent

6. Here are several examples with log base 2
log22 = 1
“log base 2 of 2 is 1”
since 21 = 2
log24 = 2
“log base 2 of 4 is 2 ”
since 22 = 4
log28 = 3
“log base 2 of 8 is 3”
since 23 = 8
log216 = 4
“log base 2 of 16 is 4”
since 24 = 16

7. Here are several examples with log base 2 continued…
log232 = 5
“log base 2 of 16 is 5”
since 25 = 32
log264 = 6
“log base 2 of 16 is 6”
since 26 = 64
log2128 = 7 “log base 2 of 8 is 7”
since 27 = 128
log2256 = 8 “log base 2 of 16 is 8”
since 28 = 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.
log33 = ___ “log base 3 of 3 is ___”
since ______
log39 = ___ “log base 3 of 9 is ___”
since ______
log327 = ___ “log base 3 of 27 is ___”
since ______
log381 = ___ “log base 3 of 81 is ___”
since ______

9. Practice set 1 of 4 answers
log33 = 1
“log base 3 of 3 is 1”
since 31 = 3
log39 = 2
“log base 3 of 9 is 2 ”
since 32 = 9
log327 = 3
“log base 3 of 27 is 3”
since 33 = 27
log381 = 4
“log base 3 of 81 is 4”
since 34 = 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.
log44 = ___ “log base 4 of 4 is ___”
since ______
log416 = ___ “log base 4 of 16 is ___”
since ______
log464 = ___ “log base 4 of 64 is ___”
since ______
log4256 = ___“log base 4 of 256 is ___” since ______

11. Practice set 2 of 4 answers
log44 = 1
“log base 4 of 4 is 1”
since 41 = 4
log416 = 2
“log base 4 of 16 is 2 ”
since 42 = 16
log464 = 3
“log base 4 of 64 is 3”
since 43 = 64
log4256 = 4 “log base 4 of 256 is 4” since 44 = 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.
log636 = ___ “log base _ of _ is ___”
since ______
log77 = ___ “log base _ of _ is ___”
since ______
log981 = ___ “log base _ of _ is ___”
since ______
log10100 = ___“log base _ of _ is ___”
since ______
log66 = ___ “log base _ of _ is ___”
since ______

13. Practice set 3 of 4 answers
log636 = 2
“log base 6 of 36 is 2”
since 62 = 36
log77 = 1
“log base 7 of 7 is 1”
since 71 = 7
log981 = 2
“log base 9 of 81 is 2”
since 92 = 81
log10100 = 2 “log base 10 of 100 is 2” since 102 = 100
log66 = 1
“log base 6 of 6 is 1”
since 61 = 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.
log101000 = ___
“_________________”
since ______
log749 = ___
“_________________”
since ______
log1010 = ___
“_________________”
since ______
log864 = ___
“_________________”
since ______
log99 = ___
“_________________”
since ______

15. Practice set 4 of 4 answers
log101000 = 3 “log base 10 of 1000 is 3”
since 103 = 1000
log749 = 2
“log base 7 of 49 is 2”
since 72 = 49
log1010 = 1
“log base 10 of 10 is 1”
since 101 = 10
log864 = 2
“log base 8 of 64 is 2”
since 82 = 64
log99 = 1
“log base 9 of 9 is 1”
since 91 = 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 longterm 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!