Calculus 9 23 2010
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Calculus-9/23/2010. Take Out: Do Now Sheet, Pencil, Homework. DO NOW: Evaluate using laws of exponents 1) 2). Agenda: -Do Now -HW Questions -Logs and Exponents powerpoint HW: Logs and Exponents Handout. Exponents , Logs. Exponents. Exponents are repeated multiplication:

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Calculus-9/23/2010

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Calculus 9 23 2010

Calculus-9/23/2010

Take Out: Do Now Sheet, Pencil, Homework

DO NOW:

Evaluate using laws of exponents

1)

2)

Agenda:

-Do Now

-HW Questions

-Logs and Exponents powerpoint

HW: Logs and Exponents Handout

Objectives: Solve complex algebraic problems using laws of logs and exponents.

Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Exponents logs

Exponents, Logs

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Exponents

Exponents

  • Exponents are repeated multiplication:

    n times

  • Example:

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Rules for exponents

Rules for Exponents

RuleExample

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Practice

Practice

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


More exponent rules

More Exponent Rules

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Practice1

Practice

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Common mistakes

Common Mistakes

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Roots

ROOTS

  • Roots don’t count as a separate category, because they are just like exponents. We’ll see why in a second.

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Root exponent connection

Root – Exponent Connection

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Practice2

Practice

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Calculus 9 23 2010

Logs

  • I want you to be able to use logs to solve for a variable.

    Things to Remember…

    If you have an exponential equation with a # base use logs to solve.

    If you have an exponential equation with base e use natural log (ln) to solve.

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Calculus 9 23 2010

Logs

  • Basic Definition of a log:

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


More log rules inverse properties

More Log Rules-Inverse Properties

BASE a:

BASE e:

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


How can we use this in an algebraic context

How can we use this in an algebraic context?

  • Whenever the variable you are looking for is in the exponent, we need to use logs

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Example 2 using inverse property

Example 2-using inverse property

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Example 3 using change of base rule

Example 3- Using Change of Base Rule

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Practice now you try either use change of base or inverse property to solve for x

Practice-Now you try either use change of base or inverse property to solve for x

  • e2x = 10

  • 54x + 1 = 15

  • 5 ex + 1 = 30

  • ex/5 + 4 = 7

  • 32x = 40

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Rules of logarithms

Rules of Logarithms

  • Since a logarithm is simply an exponent which is just being written down on the line, we expect the logarithm laws to work the same as the rules for exponents, and luckily, they do

ExponentsLogarithms

bm × bn = bm+nlogbxy = logbx + logby

bm ÷ bn = bm-nlogb (x/y) = logbx − logby

(bm)n = bmnlogb (xn) = nlogbx

b1 = blogb (b) = 1

b0 = 1 logb (1) = 0

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Example 1

Example 1

Apply product property

Change into exponential form to solve

Simplify

Reduce 1 side to zero to solve the quadratic

Factor

Solutions!!

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Example 2

Example 2

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


Example 3

Example 3

Product Property of Logs

Switch into exponential form

Simplify

Get rid of the fraction by multiplying (x-4)

Solve for x

Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.


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