Properties of LogsThe 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 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 0See this is easy

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!!!

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

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!

Properties of Logs Rule 4 blog

bx = 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?? 5log

525 = 25

12log12

144

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

Properties of Logs Try to few Use the properties to simplify each

expression. log121 log883

log100.01 log99 7log

75

32log34

= 0= 3= -3= 1= 5= 16