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Properties of Logs

Properties of Logs. The Tricky Stuff. 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. Properties of Logs. Rule 1 l og b 1 = 0

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Properties of Logs

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  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 • logb1 = 0 • If you rewrite this in exponential form, it makes sense: • b0 = 1 • What exponent always gives you 1? • So when you see this the answer is always 0! • log51 • log91 • log751 All of these equal 0 See this is easy 

  4. Properties of Logs • Rule 2 • logbb = 1 • If the base and the number are the same, the answer is 1. • Rewrite this in exponential form and it makes sense: • b1 = b • So when you see this, the answer is always 1. • log99 • log1515 • log55 All of these equal 1. Not so bad is it!!!

  5. Properties of Logs • Rule 3 • logbbx = x • A little harder, but try it thinking of it in exponential form. • Not any different than Rule 2. • log553 • 5x = 53 • x = 3

  6. Properties of Logs • Rule 3 (again) • Try again • log774 • log228 • log15159 = 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 • blogbx = 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?? • 5log525 = 25 • 12log12144

  8. Properties of Logs • Rule 7 • logbMp= plogbM • 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. • log374 = 4log37 • 3log77 = log773 • This one could be simplified further to…. • 3

  9. Properties of Logs • Try to few • Use the properties to simplify each expression. • log121 • log883 • log100.01 • log99 • 7log75 • 32log34 = 0 = 3 = -3 = 1 = 5 = 16

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