Properties of Logarithms
As mentioned above  and I can’t emphasize this enough 
logs are another way to
write exponents
. If you understand that concept it really does make things more
pleasant when you are working with logs.
Property 1
Product Rule
m
> 0 and
n
> 0
Basically, what we are saying here is that another way to write the log of a
product is to take the log of the first base and add it to the log of the second base.
Hmmmm, why don’t I just take the product of their logs??????
Wait a minute, I remember my teacher saying above that logs are another way to write exponents

WHENEVER I WAS MULTIPLYING LIKE BASES
,
I ADDED MY EXPONENTS  SO
I’M GOING TO HAVE TO ADD MY LOGS  EUREKA!!!!
Note that even though
m
and
n
are not the bases of the log itself, they can each be written as base
b
to an exponent, because of the definition of logarithms.
Here is a quick illustration of how this property works:
Property 2
Quotient Rule
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m
> 0 and
n
> 0
Basically, what we are saying here is that another way to write the log of a
quotient is to take the log of the numerator and subtract the log of the
denominator.
So here,
we have to remember that when we were dividing like bases, we subtracted our
exponents  so we do the same type of thing with our logs.
Here is a quick illustration of how this property works:
Property 3
Power Rule
m
> 0
Basically, what we are saying here is that whenever you have a 2nd exponent
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 Spring '11
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 Algebra, Exponents, Product Rule, Logarithm

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