1. The document provides instructions and examples for using the change of base formula to convert between logarithmic bases and to solve exponential equations. 2. It introduces the change of base formula and shows examples of using it to convert log bases from base-3 to base-10 using a calculator. 3. Examples are given of using the change of base formula to solve exponential equations by taking the log of both sides and applying the formula.

1. Honors Math 3
Please turn in your test corrections
Warm up
Evaluate each expression:
49log7
001.log 23
3
1
loga. b. c.
d.
Solve
2 𝑥
= 4 𝑥−6

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

4. Learning Objectives
1. Use the change of base formula to convert
logarithm bases.
2. Use the change of base formula to solve an
exponential equation.
You will need a calculator today.
Cell phones are not allowed on a test, so please invest in a
calculator if you do not already have one.

5. Introduction
We can solve this easy without
a calculator:
x27log3
3x
What about this?
4log3
43 x
3 raised up to WHAT power gives 4?:

6. I dunno!

7. Can I solve it with
a calculator?
Yes you can!
With The Change
of Base
Formula

8. LOG
Remember on the
calculator the key that
looks like this? :
That only works for one base!
Base 10Better known as the
“common” log.

9. Our calculator has the
base-10 Log
programmed for every
number
Example: 22log
Answer: 1.34
4log3
From base-3, to base-10?
Maybe we can use that
fact to convert

10. Introducing….
The Change of Base Formula
a
x
x
b
b
a
log
log
log 
Now we can solve our logarithm.
What it means:
I can convert the logarithm of a
base I don’t know into a
fraction of 2 logarithms of a
base that I DO know.

11. Let’s use the change of base formula
to convert the log from base-3 to
base-10:
a
x
x
b
b
a
log
log
log The change of
base formula is:
4log3
3log
4log
10
10
Use your calculator
to solve:
262.14log3 

12. We could have made it any other base besides
base 10 , but 10 is more practical and useful:
a
x
x
b
b
a
log
log
log The change of
base formula is:
4log3
Base π :
log 22 4
log 22 3Base 22:
4log3
log π 4
log π 3
Kind of cool, but you can’t really put in most calculators.

13. 40log3
9log2
2
1
log7
2log
9log
10
10
 169.3
357.3
356.
3log
40log

7log
2
1
log


14. Solving Equations using change of base

15. To solve an exponential equation that can’t be solved
using the one to one property, take the log of both
sides.
Solve for X: 532
x

16. Solve for X:
To solve an exponential equation, take the log of both
sides
382
x

17. Solve for X:
To solve an exponential equation, take the log of both
sides
52𝑥−1
4
= 2.66

18. Solve for X:
26.1log x623.log x