1. Properties of Logs The Tricky Stuff

2. Properties of Logs  Look at the sheet.  We will be focusing on rules 1 – 4 and 7.  Do not lose this sheet!!  You can use it for quizzes and tests.  You will need it for a while.

3. Properties of Logs  Rule 1  log b 1 = 0  If you rewrite this in exponential form, it makes sense:  b 0 = 1  What exponent always gives you 1?  So when you see this the answer is always 0!  log 5 1  log 9 1  log 75 1 All of these equal 0 See this is easy

4. Properties of Logs  Rule 2  log b b = 1  If the base and the number are the same, the answer is 1.  Rewrite this in exponential form and it makes sense:  b 1 = b  So when you see this, the answer is always 1.  log 9 9  log 15 15  log 5 5 All of these equal 1. Not so bad is it!!!

5. Properties of Logs  Rule 3  log b b x = x  A little harder, but try it thinking of it in exponential form.  Not any different than Rule 2.  log 5 5 3  5 x = 5 3  x = 3

6. Properties of Logs  Rule 3 (again)  Try again  log 7 7 4  log 2 2 8  log 15 15 9 = 4 = 8 = 9 So the rule really just says: When the base and the number are the same, the answer is the exponent!

7. Properties of Logs  Rule 4  b log b x = x  So if for some reason you want to raise a number to a log and that log has the same base as the number, the answer is the number in the log.  WHAT??  5 log 5 25 = 25  12 log 12 144

8. Properties of Logs  Rule 7  log b M p = plog b M  I call this “peeing on the log”.  When you have a power on the number, you can bring it out in front of the log or vice versa.  log 3 7 4 = 4log 3 7  3log 7 7 = log 7 7 3  This one could be simplified further to…. 33

9. Properties of Logs  Try to few  Use the properties to simplify each expression.  log 12 1  log 8 8 3  log 10 0.01  log 9 9  7 log 7 5  3 2log 3 4 = 0 = 3 = -3 = 1 = 5 = 16