This document contains a pre-calculus warm up exercise evaluating logarithmic expressions, followed by some jokes. It then introduces the change of base formula for logarithms, explaining that it allows converting a logarithm from an unknown base to a base that a calculator can evaluate like base 10. It provides examples of using the formula to evaluate logarithmic expressions with unknown bases by converting them to base 10.

1. Pre calculus Warm up
October 24, 2011
Evaluate each expression:
a.
log 7 49
d.
2
3 3
b.
x
log .001
x
e.
5
5y
c.
1
ln 2
e

2. And now it’s time for..
The Lame Joke of the day..
How do we know that the following fractions
are in Europe? A/C, X/C, and W/C?
Because their numerators are all over C’s!

3. And now it’s time for..
The Lame Joke of the day..
Where does a Bee go to the bathroom?
A BP Station!

4. Introduction
We can solve this easy
without a calculator:
log 3 27
x
x
3
What about this?
log 3 4
3 raised up to WHAT power gives 4?:
3
x
4

5. I dunno!

6. Can I solve it with
a calculator?
Yes you can!
With
Th
e
Change of
Base
Formula

7. Introducing….
The Change
of
Base
What it says:
Formulalog
x
log a x the
I can convert
log b a
b
logarithm of a base I
don’t know into to a
fraction of 2 logarithms
Nowa base solve our logarithm.
of we can that I DO know.

8. Let’s use the change of base
formula to convert the log
log
from base-3
The change of to base-10: b x
base formula is:
log 3 4
log 10 4
log 10 3
log a x
log b a
Use your calculator
to solve:
log 3 4
1.262

9. log 2 9
log 10 9
log 10 2
3.169
log 3 40
log 40
log 3
3.357
1
log 7
2
1
log
2
log 7
.356

10. log 2 9
log 10 9
log 10 2
3.169
log 3 40
log 40
log 3
3.357
1
log 7
2
1
log
2
log 7
.356