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

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

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

Exponential and Exponential and Logarithmic FunctionsLogarithmic Functions

P. Hinlo GUHS 4

Learning ObjectivesLearning Objectives

Use and apply properties of logarithms to simplify equations

P. Hinlo GUHS 5

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

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

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

P. Hinlo GUHS 8

Properties of Exponentials Properties of Exponentials and Logarithms and Logarithms

y = logax ay = x

ay = x y = logax

ax = ex ln a

P. Hinlo GUHS 9

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

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

P. Hinlo GUHS 11

Practice:Practice:

Simplify without a calculator. In other words, let’s use what we know about logarithms!

2/20/2003 TCSS320A Isabelle Bichindaritz 12