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Properties of Logarithms

# Properties of Logarithms - Properties of Logarithms As...

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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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