GRANT UNION HIGH SCHOOL

# GRANT UNION HIGH SCHOOL

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## GRANT UNION HIGH SCHOOL

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1. GRANT 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

2. COLLABORATION 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

3. TEACHER 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

4. Exponential and Logarithmic Functions P. Hinlo GUHS

5. Learning Objectives • Use and apply properties of logarithms to simplify equations P. Hinlo GUHS

6. 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

7. 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

8. 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 P. Hinlo GUHS

9. Properties of Exponentials and Logarithms y = logax  ay = x ay = x  y = logax ax = ex ln a P. Hinlo GUHS

10. Exponential and Logarithmic Equations Solve 85x+1 = 182x-3e 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

11. Exponential and Logarithmic Equations 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 72x = e (ln 3 . ln 2 / ln 72)= 3 ln 2 / ln 2.36 = 3 ln 2 / ln 2.2.2.3.3 P. Hinlo GUHS

12. Practice: Simplify without a calculator. In other words, let’s use what we know about logarithms! TCSS320A Isabelle Bichindaritz