# Laws of Logarithms

May 14th, 2015
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YOU MUST LEARN THESE! If m, n and b are positive numbers, b ≠ 1 then 1. log b = 1 2. log 1 = 0 3. log (PQ) = log P + log Q 4. logb âŽœ âŽŸ = logb P − logb Q

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1310 Notes 5o4 fill2M 131015.4Math 1310Section 5.4Laws of LogarithmsThe laws:YOU MUST LEARN THESE!If m, n and b are positive numbers, b 1 then1. log b = 1b2. log 1 = 0b3. log (PQ) = log P + log QbbbP4. logb = logb P logb QQ1Note: logb = logb Q Why?Q5. log Pn = n log Pbb6. blogb P = P7. log bP = Pb8.(Change of base formula)logb xloga x =logb aNote: this results inln x .loga x =ln aExamples using these properties:M 131025.4Errors to avoid:loga (x + y) loga x + loga yloga x loga x loga yloga y(loga x)3 3 loga xUsing the properties to simplify logarithmsExample 1: Simplify each logarithmlog2 (32)log6 9 + log6 4log4 ( 96 ) log4 (6) 1log3 81 ( )log2 46logb( b)( ) 1 loga loga a2 a3 M 131035.4Separating One Complicated Logarithmic Expression:Example 2: Rewrite the expression in a form with no logarithm of a product, power, or quotient.log3 (x(x + 4))Example 3: Rewrite the expression in a form with no logarithm of a product, power, or quotient.log3xlog ( 3x )Example 4: Rewrite the expression in a form with no logarithm of a product, power, or quotient. ab3 ln c2 d M 131045.4Example 5: Rewrite the expression in a form with no logarithm of a product, power, or quotient.

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