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Lesson22 - Summer MA 15200 Lesson 22 Section 4.3 This...

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1 Summer MA 15200 Lesson 22 Section 4.3 This lesson is on the properties of logarithms. Properties of logarithms model the properties of exponents. I Product Rule Product Rule of Exponents : m n m n b b b + = Notice: When the bases were the same, the exponents were added when multiplication was performed. Likewise logarithms are added when multiplication is performed in the argument. Product Rule of Logarithms : log ( ) log log b b b MN M N = + In words, the logarithm of a product is the sum of the logarithms. When a single logarithm is written using this product rule, we say we are expanding the logarithmic expression. Ex 1: Assume all variables represent positive values. Use the product rule to expand each expression and simplify where possible. ( ) 2 2 5 ) log (7 ) ) log 2 ) log(100 ) ) ln(20 ) b a r b x y c ab d e = = = = II Quotient Rule Quotient Rule for Exponents : m m n n b b b = Notice: When the bases were the same, the exponents were subtracted when division was performed. Likewise, logarithms are subtracted when division is performed in the argument.
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