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Factoring Warm-up
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Properties of Logarithms
Section 7-5 Properties of Logarithms
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Objectives I can expand log expressions using log properties
I can condense log expressions using properties
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3 Main Properties Product Property Quotient Property Power Property
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Product Property logb mn = logb m + logb n
You can use this property from left to right or from right back to the left. Left to Right (Expanding) Right to Left (Condensing)
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Product Rule log2 4x = log2 4 + log2 x
This is called expanding a log expression
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Working Backwards log3 x + log3 3 + log3 9 log3 3x + log3 9 log3 27x
This is called condensing an expression
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Quotient Property logb m/n = logb m – logb n Left to Right (Expanding)
Right to Left (Condensing)
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Quotient Rule This is Expanding
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Working Backwards log3 x - log3 3 log3 x/3
This is called condensing an expression
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Power Property logb mp = p logb m Left to Right (Expanding)
Right to Left (Condensing)
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Power Rule log2 x3 = 3log2 x This is Expanding
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Conversions
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BIG Picture Positive Logs (Numerator) Negative Logs (Denominator)
Don’t leave fractional exponents
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Condensing
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Condensing
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Homework Worksheet 11-8
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