SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x =...

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SOLVING LOGARITHMIC AND INDICES PROBLEM

Transcript of SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x =...

Page 1: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

SOLVING LOGARITHMIC AND INDICES PROBLEM

Page 2: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

Solving equation in the form of ax = ay

Example:

32x = 27 = 33

By comparing index:

2x = 3

If ax = ay then x = y

23x

Page 3: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

Examples

8x+1 = 4x+3

(23)x+1 = (22)x+3

23x+3 = 22x+6

By comparing index: 3x + 3 = 2x + 6 3x – 2x = 6 – 3 x = 3

Page 4: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

9x. 3x1 = 243

32x. 3x1 = 35

32x + (x 1) = 35

33x1 = 35

By comparing index, 3x – 1 = 5 3x = 6 x = 2

Examples

Page 5: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

SOLVE 2X + 2X+3 = 32

See the right way ---->

A very different example. 2X + 2X+3 = 25

x + x + 3 = 5 2x = 2 x = 1WARNING! WARNING! WARNING!The solution above is WRONG!!!

Page 6: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

2x + 2x 23 = 32Factorize 2x

2X(1 + 23) = 322X (9)= 322X = 32/9X lg 2 = lg 32 – lg 9X (0.3010)= 1.5051-0.9542

X=1.8302

SOLVE 2X + 2X+3 = 32

Page 7: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

INDEX EQUATION WITH DIFFERENT BASEIf we cannot express both sides of the equation with the same base, we solve the equation by taking logarithms on both

sides.

Example

5 x = 6Taking logarithms on both sides.

log10 5 x = log10 6

x log10 5 = log10 6

x (0.6990) = 0.7782 x = 0.7782 0.6690 x = 1.113

Solving equation in the form of ax = b,where a ≠-1, 0 , 1

Page 8: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

Example: Solve 5x – 3x+1 = 0Solution:

5x – 3x+1 = 0 5x = 3x+1

Taking logarithms on both sides,

lg 5x = lg 3x+1

x lg 5 = (x + 1) lg 3

x lg 5 = x lg 3 + lg 3

x lg 5 – x lg 3= lg 3

x(lg 5 – lg 3)= lg 3

x(0.6990 – 0.4771) = 0.4771

x = 2.150

Page 9: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

Solving Logarithmic EquationSolve log5 (5x – 4) = 2 log5 3 + log5 4

First, simplify the right hand side.

log5 (5x – 4) = log5 3

log5 = log5

Comparing number in both sides.

log5 log5

5x = 40

x = 8

(5x – 4 ) (36)

2 + 4log

55

(5x – 4) == (36)

Page 10: SOLVING LOGARITHMIC AND INDICES PROBLEM. Solving equation in the form of a x = a y Example: 3 2x = 27 = 3 3 By comparing index: 2x = 3 If a x = a y then.

Solve the equation log5 x = 4 logx 5

Solution:

log5 x = 4

log5 x. log5 x = 4

(log5 x)2 = 4

log5 x = 2 or -2

x = 52 or 5 2

xlog15

(Change base from x to 5)


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Assembly instructions · 2019-02-06 · 2096 3 619 2x 2x 2x 2x 2100 2 3 425 2x 2x 2x 2x 3021 5 1800 2x 2x 2x 2x 3032 1A/B 1350 6x 8x 10x 12x Item No. Part Sect. Ref. Size mm Quantity

Solving Quadratic Equations - E.L.F. Software quad.pdf · name date period Batch 50532dbd Solving Quadratic Equations Version 3 Example: (x+2)(2x 3) = 0 has the solution x 2f 2;1:5g

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Holt McDougal Algebra 1 5-4 Solving Special Systems Warm Up Solve each equation. 1. 2x + 3 = 2x + 4 2. 2(x + 1) = 2x + 2 no solution infinitely many solutions.

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Solving Multi-Step Equationsgbhsguidance.weebly.com › uploads › 1 › 0 › 7 › 9 › 107900997 › algeb… · Solving Multi-Step Equations Ex: 3(2x - 5) - 3 = 2x + 8 + 6x

Solving Multi-Step Equationsgbhsguidance.weebly.com › uploads › 1 › 0 › 7 › 9 › 107900997 › algeb… · Solving Multi-Step Equations Ex: 3(2x - 5) - 3 = 2x + 8 + 6x

Equations Solving problems: x + x + 1= 43 2x +1 -1 = 43 – 1 2x = 42 2 2 Solution: x = 21.

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Practice solving systems by graphing 1.)2.) 2x + 5y = –5 x + 3y = 3.

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10698...1 10698 2 3 2x 1 1x 2 4 2x 3 1x 4 2x 5 2x 5 1x 6 6 2x 7 7 2x 3x 8 1 2 8 2x 9 9 2x 10 1x 11 10 2x 12 2x 13 11 2x 14 2x 15 12 13 Created Date 6/13/2017 12:39:41 PM ...

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NATIONAL SENIOR CERTIFICATE EXAMINATION · PDF fileArea DGEF = DE x EF = x tan 60 ⁰ (3 – 2x) = x. 3.(3 – 2x) = 3.x (3 – 2x) EF = 3 – 2x x tan 60⁰ (3 – 2x) (2) 8.3 A(x)

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72006 - Lego72006. 2 3 4. 3 2x 3 25. 4 2x 1x 1x 26 1x 27 1x 1x 28. 5 2x 29 7 2x 30 2x 7 1:1 7 7. 6 31. 7 2x 2x 32 2x. 8 4x 2x 33 1 2 2x. 9 2x 4x 34. 10 2x 2x 35 2x. 11 2x 2x 36. 12

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LESSON 2.3 – PROBLEM SOLVING...3x + 3 = 7 + 2x + 4 3x + 3 = 2x + 11 x + 3 = 11 x = 8 So the smallest number is 8. You can check that 8 + 9 + 10 = 7 + 2 10. Notice that this is the

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Drill: Find dy/dx y = x 3 sin 2x y = e 2x ln (3x + 1) y = tan -1 2x Product rule: x 3 (2cos 2x) + 3x 2 sin (2x) 2x 3 cos 2x + 3x 2 sin (2x) Product Rule.

3- Solving by Substitution - Miss Zukowski's Class...3) solving by substitution Warm-Un: Solve the system of equations graphically and verify algebraically. 2x+y=5 x+Y-3=O Solution:

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Using Problem Solving Strategies and ModelsYour Notes Solve ⏐2x 1 5⏐> 3. Then graph the solution. The absolute value inequality is equivalent to 2x 1 5 < or 2x 1 5 > .

Using Problem Solving Strategies and ModelsYour Notes Solve ⏐2x 1 5⏐> 3. Then graph the solution. The absolute value inequality is equivalent to 2x 1 5 < or 2x 1 5 > .