Warmup Alg 227 Feb 2012

Warmup Alg 228 & 29 Feb 2012

Agenda• Don't forget about resources on

mrwaddell.net• Assignment from last class period• Sect 7.6: Solving log equations

Go over assignment from last class period

Section 7.6: solving log equations

Vocabulary

Exponentials

Logarithm

log x

ln x

Any equation of the form y=(b)x

The opposite of an exponential equation

x= logb y

No base? It is automatically base 10!

“ln” is a shortcut way to writeloge or log base e

Exponents First – Page 330

Product Property

logb (mn) = = logb m + logb n

Quotient Property

logb =nm

= logb n – logb m

Power Property

logb mp =THIS IS EASILY THE MOST IMPORTANT ONE!

= p logb m

Inverse Properties (2 of them)

logb bx = x xb xb log

Help! Where to find it.

Example problem

4x = 2x-2 The problemIf the sides had the samebase, we could do it! (22)x = 2x-2

A little simplification 22x = 2x-2

Equality rule! 2x = x-2

Regular algebra (find a zero)and subtract x from both sides

x = -2

Example problem – You try

92x = 27x-1 The problemIf the sides had the sameexponent, we could do it! (32)2x = (33)x-1

A little simplification 34x = 33x-3

Equality rule! 4x = 3x-3

Regular algebra (find zerosand ones)

x = -3

Another example

4x = 11The problemTake the log base 4 of Both sides (why base 4?) log44x = log411

x = log411Equality rule!

x ≈ 1.73Use calculator to find theanswer.

log1011log104

x = Here is how to do it, if youDon’t have an nSpire:

Another example – You Try

79x = 15The problemTake the log base ? of Both sides (why base ??) log779x = log715

9x = log715Equality rule!

x ≈

Use calculator to find theanswer.

log1015log107

x = / 9Here is how to do it, if youDon’t have an nSpire:

x = (log715) / 9

Using Logs to solve

log5(4x-7) = log5(x+5) The problem

Normal algebra from here

Equality rule!

Add 7, subtract x, divide By 3

(4x-7) = (x+5)

4x = x+12

3x = +12

x = 4

Using Logs to solve

log2(x-6) = 5 The problem

Normal algebra from here

USE THE DEFINITIONOF A LOG! 25 = x – 6

32 = x – 6

38 = x

Complex ProblemSolve for x.

problem2log7x + log72 = log7(5x+3)

log7x2 + log72 = log7(5x+3) Power prop

log72x2 = log7(5x+3) Product prop

2x2 = (5x+3) 1 to 1 prop

2x2 -5x - 3 = 0 Solve the quadratic (2x+1)(x-3) = 0

x = -1/2 and x = 3Double check if you get 2 answers!Or graph the original to check!

Assignment

Chapter 7.6:

6 – 11,

15 – 20,

24 – 27