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-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

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 72 x = e (ln 3 . ln 2 / ln 72) = 3 ln 2 / ln 2.36 = 3 ln 2 / ln
P. Hinlo GUHS

12. TCSS320A Isabelle Bichindaritz
Practice:
Simplify without a calculator. In other words, let’s use what we know about logarithms!
2/20/2003
TCSS320A Isabelle Bichindaritz