GRANT UNION HIGH SCHOOL
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Transcript of GRANT UNION HIGH SCHOOL
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GRANT UNION HIGH SCHOOLGRANT UNION HIGH SCHOOL• Title I school • 2,000 – 2,200 student population• 90% of students have free lunch (low social
economic status)• 40% of student population are English Language
Learners (Hispanic; Hmong and Lao refugees)are Special Education
• At least 30% of students don’t live with parents (foster home, relatives)
• Math skills of almost 50% of student population is 1 to 2 grade levels behind
P. Hinlo GUHS 1
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COLLABORATION GOALSCOLLABORATION GOALS• 70% of students in each class achieve in math
• Weekly collaboration to discuss lesson delivery, teaching strategies, assessment results, and make revisions to plans as needed
• Standards-driven reform is the primary approach
• Activate student conceptual knowledge when presented with a real-life problem solving situation
• Improve student motivation, participation, and generalization skills
P. Hinlo GUHS 2
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TEACHER COLLABORATIONTEACHER COLLABORATION• Involves teachers of same subject matter• Weekly collaboration to discuss lesson
delivery, teaching strategies, assessment results, and make revisions to plans as needed
• Standards-driven reform is the primary approach
• Planning for curriculum, pacing, common formative assessments, sharing of best practices during summer break
P. Hinlo GUHS 3
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Exponential and Exponential and Logarithmic FunctionsLogarithmic Functions
P. Hinlo GUHS 4
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Learning ObjectivesLearning Objectives
Use and apply properties of logarithms to simplify equations
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Logarithmic Functions Logarithmic Functions Logarithmic function: the logarithmic function is
the inverse of the exponential function.
Logarithmic function of base b: f(x) = logbx , for b 1.
f(x) = logbx f-1(x) = bx where b 1, and x is any real number.
a = logbc ba = c, where b 1.
Domain: (0, +) (the range of exp).
Range: R (the domain of exp).
P. Hinlo GUHS 6
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Properties of Logarithms Properties of Logarithms For a,b >0, b 1
logax = logbx a = b logan = logam n = m
The logarithm is a one-to-one function.
logbbx = x b logb x = x logb1 = 0
logbx = ln(x) / ln(b)
P. Hinlo GUHS 7
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Properties of Logarithms Properties of Logarithms
logb (ac) = logb a + logb c
logb (a/c) = logb a - logb c
logb (ac) = c logb a
logb (a) = logc a / logc b
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Properties of Exponentials Properties of Exponentials and Logarithms and Logarithms
y = logax ay = x
ay = x y = logax
ax = ex ln a
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Exponential and Logarithmic Exponential and Logarithmic EquationsEquations
Solve
85x+1 = 182x-3 e ln (8) (5x+1) = eln(18) (2x-3)
ln(8) (5x+1) = ln(18) (2x-3)
x (5ln8 –2ln18) = -3ln18 – ln8)
x = - (3ln18 + ln8) / (5ln8 – 2ln18)
P. Hinlo GUHS 10
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Exponential and Logarithmic Exponential and Logarithmic EquationsEquations
Solve
log2 8 + log2 9 = logx 3
log2 (8 . 9) = logx 3
ln (72) / ln 2 = ln3 / ln x
ln x = ln 3 . ln 2 / ln 72
x = e (ln 3 . ln 2 / ln 72)
= 3 ln 2 / ln 2.36 = 3 ln 2 / ln 2.2.2.3.3
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Practice:Practice:
Simplify without a calculator. In other words, let’s use what we know about logarithms!
2/20/2003 TCSS320A Isabelle Bichindaritz 12