Sec 54-filled

# Sec 54-filled - Math 1310 Section 5.4 Properties of...

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Math 1310 Section 5.4 Properties of Logarithms You will sometimes be asked to rewrite logarithmic expressions in either an expanded or contracted form. To do this, you will use the Laws of Logarithms. You must know all 8 of the Laws of Logarithms. Laws of Logarithms If m , n and b are positive numbers, 1 b , then 1. n m mn b b b log log log + = 2. n m n m b b b log log log - = 3. m n m b n b log log = 4. 0 1 log = b 5. 1 log = b b 6. x b x b = log 7. x b x b = log 8. b m m b log log log = (change of bases formula) These properties are true for logs of any base, including common logs and natural logs. Example 1: Rewrite each of the following expressions in a form that has no logarithms of a product, quotient or power. a. x 5 log 3 b. ( 29

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Sec 54-filled - Math 1310 Section 5.4 Properties of...

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