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SOLVING (expand and condense)
3.3: Properties of Logs SOLVING (expand and condense)
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3.3 Properties of Logarithms
Essential Questions: How can I use the properties of logarithms to expand, condense, and solve logarithmic equations?
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1st Type of Logarithm: Common Log ο π₯π¨π π =π Examples:
If there is no βbβ term, the log has base 10. Examples: log 45 = ____ log = ____ log ΒΎ = _____ 1.65 .507 -.125
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2nd type of Logarithm: Natural Log ο π₯π§ π =π ln 4 loge4 = ___________
ln implies a base of βeβ ln 4 loge4 = ___________ Examples: Ln 5 = _____ Ln 3.144= _____ Ln 5/8 = _____ 1.61 1.45 -.47
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Laws of Natural Logarithms
ln XY = ln X + ln Y Product: Quotient: Power: One-to-One: Identity: ln π π = ln X β ln Y ln XY = Y ln X If ln X= ln Y, then X = Y If ln ex = x
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Expand the logarithmic expression:
a) ln 7 π¦ 3 4 π₯ 3 ln ln y β ln 4 β 3 ln x OR ln ln y β (ln ln x) b) ln 6 π₯ 2 π¦ 4 ln ln x β 4 ln y
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c) ln 6 π (1/2)ln6 β (1/2)lnb d) ln 4w 3 π₯ 2 ln4 + lnw + (2/3)lnx
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Condense to a single logarithm
a) 5 ln(x + 1) + ln x b) 6 ln(x β 4) + 3 ln x c) ln (3x + 5) β 4ln x β 6ln(x β 1) ln x(x + 1)5 ln x3(x β 4)6 ln 3π₯+5 π₯ 4 (π₯β1 ) 6
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One-to-One and Identity equations
Solve for x. a) ln 3 π₯ 2 = ln 4 b) ln ex+1 = 4 3 π₯ 2 =4 x + 1 = 4 x = 3 x2 = 64 x = Β± 8
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Homework 3.3 Properties of Logs Worksheet
βNo, not my dog. I do my homework on my computerβ¦and the cat ate the mouse.
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