pg. 301/308/311 homework study #8right 2; x = 2#10reflect y; right 5; x = 5 #12right 4/3; up log 2...

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Pg. 301/308/311 Homework • Study • #8 right 2; x = 2 #10 reflect y; right 5; x = 5 • #12 right 4/3; up log 2 3; x = 4/3 #14 reflect x; left 3; down 2; x = -3 • #16 D: (-3, ∞); R: (-∞, ∞) #18 D: (-∞, 0); R: (-∞, ∞) • #20 Graph #1 x = 10,000 #2 x = 1/e • #3 x = 5.25 #4 x = ½ #5 x = 97 • #6 x = 1001 #7 x = 16 #8 x = 531,434 • #9 x = 3 #10 x = 2 4/3 #11 x = e 3 /2 • #12 x = 80 #13 x = 1 #14 x = 1/3 • #41 $701.28 #42 $707.39 • #43 $708.81 #44 $708.51 • #45 $705.30 #46 $709.53

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Page 1: Pg. 301/308/311 Homework Study #8right 2; x = 2#10reflect y; right 5; x = 5 #12right 4/3; up log 2 3; x = 4/3#14reflect x; left 3; down 2; x = -3 #16D:

Pg. 301/308/311 Homework• Study

• #8 right 2; x = 2 #10 reflect y; right 5; x = 5• #12 right 4/3; up log23; x = 4/3 #14 reflect x; left 3; down 2; x = -3• #16 D: (-3, ∞); R: (-∞, ∞) #18 D: (-∞, 0); R: (-∞, ∞)• #20 Graph #1 x = 10,000 #2 x = 1/e • #3 x = 5.25 #4 x = ½ #5 x = 97• #6 x = 1001 #7 x = 16 #8 x = 531,434• #9 x = 3 #10 x = 24/3 #11 x = e3/2• #12 x = 80 #13 x = 1 #14 x = 1/3 • #41 $701.28 #42 $707.39• #43 $708.81 #44 $708.51• #45 $705.30 #46 $709.53

Page 2: Pg. 301/308/311 Homework Study #8right 2; x = 2#10reflect y; right 5; x = 5 #12right 4/3; up log 2 3; x = 4/3#14reflect x; left 3; down 2; x = -3 #16D:

5.6 Solving Logarithmic Equations

How to Solve a Logarithm• In order to solve a logarithm,

you must use the properties discussed to simplify the problem as best possible.

• Then each side must be raised to a power or have a logarithm taken, and you will be able to easily solve for x.

• Make sure you check for extraneous solutions!

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log log 2 1x x

5 5

1log 6 log 02

x x

2 2 2log 2 1 log 3 2log 3x x

3 1.08x

Page 3: Pg. 301/308/311 Homework Study #8right 2; x = 2#10reflect y; right 5; x = 5 #12right 4/3; up log 2 3; x = 4/3#14reflect x; left 3; down 2; x = -3 #16D:

Ch. 5 Review

Things to know:• Solving radicals• Graphing exponentials• Solving exponentials• Population• Half-Life• Simple Interest • Compound Interest• Log properties• Graphing logs• Solving Logs• Word Problems!!

Hints!• What are the basic “knows”

of exponential functions and logarithmic functions?

• Rewriting in terms of a variable (like the soda can!)

• Think about sign patterns with exponentials and logs! When are they <,> zero?

• Know your properties!!!

Page 4: Pg. 301/308/311 Homework Study #8right 2; x = 2#10reflect y; right 5; x = 5 #12right 4/3; up log 2 3; x = 4/3#14reflect x; left 3; down 2; x = -3 #16D:

Ch. 5 Review

Solve the following:• Solve for the variable. Make

sure to check for extraneous solutions!

Graph the following:• State the transitions and/or

reflections that occur and the domain and range.

ln 2 1y x

2 3 xy

log 4 2y x

5 5log log 4 1x x 1 32 4x

5 3 2x x

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9 3 X 9 X (D) 9 X 2 (E) 3 X 2

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EE 553 Integer Programming J. McCalley 1. Solving IPs Minimize f(x 1, x 2, x 3 ) Subject to h(x 1, x 2, x 3 )=c g(x 1, x 2, x 3 )≤b x 1, x 2, x 3 are

DISC HARROW NUAL - Woods Equipment Company and Channel 3" x 3" Tube 3" x 3" Tube Disc Gang Tube 2" x3" 2" x 3" 2" x 3" 3" x 3" 3" x 3" ... manufacture of our products. ... nuts and

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3 x 2 x SECS 5 3 x 2 x SECS 5 1 x 1 x ... - Rollease Acmeda

8.1 Completing a Square Given: x 2 = u x = +√(u) or x = -√(u) E.g. Given: x 2 = 3 x = √(3) or x = -√(3)

Warm-up, 3/28 Compute: 1. 2 x 2 x 2 x 2 = 2. 3 x 3 x 3 = 3. 2 x 2 x 3 x 3 x 3 = 4. 5 x 5 x 2 x 2 = 5. 2 x 2 x 4 =

Determinants of 2 x 2 and 3 x 3 Matrices

Factorising Cubics (Example 1) Factorise x 3 + 7x 2 + 7x 15 given that (x + 3) is a factor x 3 + 7x 2 + 7x 15 = (x + 3)(x 2 + ax 5) x 3 + 7x 2 +

Cluster structure on K-theoretic Coulomb branchesart/data/StringMath/F20/Coulomb-branch… · p 1 + x 1 x 2 x 1 x 3 x 2 x 4 x 3 p 1 p 2 + x 1 x 2 p 2 p 3 + x 2 x 3 p 3 p 4 + x 3 x

ISSN: 0975-766X CODEN: IJPTFI Available Online through ... · 2−65,2708∙(x 2) 2+28,229∙(x 3) 2--6,25∙x 1∙x 2+7,5∙x 1∙x 3+0,75∙x 2∙x 3 Using the obtained regression

X 2 + 2 = 11 X 2 = 9 X = 3 Check: X 2 + 2 = 3 x 3 +2 = 11 We can solve this equation by:

2 x 6= 2 x 2= 2 x 9= 2 x 3 - Homeschool Den

Factoring x 2 = 9 x 2 - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 x = {-3, 3} Zero-factor property

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