1. Ch. 3.3 Properties of Logarithms
Objectives:
1.) To learn and practice using the change of base theorem
2.) Solving exponentials with the change of base theorem

2. Warm-up Solve the equations and simplify the expressions
1.) 3x = 27 2.) log4 + log39 3.) 25x+2 =125 4.) lnex + 4 = 2 5.) log log232

3. Vocabulary Common logarithm/common log: A logarithm with base 10
Natural logarithm/ natural log: A logarithm with base e

4. Consider 3x = 27 Common Base Method 3x = 33 Common Base implies x = 3
Writing as a logarithm and using the change of base property
log33x = log327
=> x = log327

5. Change of Base Theorem pg 219
The change of base theorem will allow you to take a logarithm with a certain base b, and write it as a quotient or ratio of logarithms of a different base.
=> x = log327

6. What if I asked you to simplify
10 x = 35
2x = 3
log or log23
What’s your problem? What?

7. 10 x = 35 2x = 3 log1010x = log1035 log22x = log23

8. Homework
Pg. 223 #1-3; (even; write the exponential equation you would be solving for); 76-80(even) Page 232 #2,5, 9-14; 24-28; 31-36; 46-50