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### Exponents, Logs

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.

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 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

Rule 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.

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

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.

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.

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.

- 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.

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.

- Basic Definition of a log:

More Log Rules-Inverse Properties 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.

BASE a:

BASE e:

How can we use this in an algebraic context? 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.

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

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 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 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.

- e2x = 10
- 54x + 1 = 15
- 5 ex + 1 = 30
- ex/5 + 4 = 7
- 32x = 40

Rules of Logarithms property to 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.

- 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

Example 1 property to 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.

Apply product property

Change into exponential form to solve

Simplify

Reduce 1 side to zero to solve the quadratic

Factor

Solutions!!

Example 2 property to 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.

Example 3 property to 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.

Product Property of Logs

Switch into exponential form

Simplify

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

Solve for x

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