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# Akar, pangkat dan logaritma

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### Akar, pangkat dan logaritma

1. 1. INDICES, SURDAND LOGARITHM LYDIA VALENSIAEmail : lydia.valensia@yahoo.com SMA NEGERI 2 SEKAYU
2. 2. INTRODUCTION LET’S EXPLORE “INDICES, SURDS AND LOGARITHM” COMPETENCES INDICATOR MATERIAL EVALUATION
3. 3. INTRODUCTION Are you smarter than 9th grader? COMPETENCES INDICATOR DO YOU KNOW ? MATERIAL EVALUATION
4. 4. INTRODUCTION Are you smarter than 9th grader? COMPETENCES Math Aptitude Test INDICATOR Which of the following sentences is correct? Nine and five are thirteen. or MATERIAL Nine and five is thirteen. EVALUATION Solution: Neither is correct , 9 + 5 = 14
5. 5. INTRODUCTION DO YOU KNOW? COMPETENCES History How did we get the word "Surd" ? INDICATOR Well around 820 AD al-Khwarizmi (the Persian guy who we get the name "Algorithm" from) called irrational numbers MATERIAL "inaudible" ... this was later translated to the Latin surdus ("deaf" or "mute") EVALUATION
6. 6. INTRODUCTIONCOMPETENCES STANDARD COMPETENCE: 1. Solving problems related to indices, surds and INDICATOR logarithms BASIC COMPETENCE: MATERIAL Using laws of indices, surds and logarithms. Doing the algebraic manipulation in computation related to indices, surds EVALUATION and logarithms. (Integrated with E- SETS )
7. 7. INTRODUCTIONCOMPETENCES INDICATOR INDICATORS: All of students should be able to: MATERIAL 3.Change indices to surds or vice versa. 4.Change indices or surds to logarithms form 5.Finish the computation related to indices, surds and logarithms. EVALUATION
8. 8. MATERIAL INDICES Indices or powers are also called exponent The exponent of a number say how many times to use the number in multiplication. In example 82 = 8 x 8 = 64 In words: 82 could be called “8 to the second power”, “8 to the power 2” or simply “8 squared”. Example : 116 is easier to write and read than 11 x 11 x 11x 11 x 11x 11
9. 9. MATERIAL INDICES Let b be a real number or a variable representing a real number. Let n be a positive integer. bn = b·b·b·b···b where there are n b’s example: 85 = 8·8·8·8·8 Example: x4 = x·x·x·x In general:
10. 10. MATERIAL Law Example INDICES x1 = x 61 = 6 x0 = 1 70 = 1 x-1 = 1/x 4-1 = ¼ xmxn = xm+n x2x3 = x2+3 = x5 xm/xn = xm-n x4/x2 = x4-2 = x2 (xm)n = xmn (x2)3 = x2×3 = x6 (xy)n = xnyn (xy)3 = x3y3 (x/y)n = xn/yn (x/y)2 = x2 / y2 x-n = 1/xn x-3 = 1/x3
11. 11. MATERIAL SURDS If it is a root and irrational, it is a surd. But not all roots are surds. f a, b, (a ≠ 0 and b ≠ 0 are positive) and (m and n are real numbers) then 1. Multiplication of Surds : 1 1 1 a x b = a x b = ( a x b ) = ab 2 2 2 2. Division of Surds 1 1 a a2 a 2 a 2. a: b = = 1 =  = b b b b2
12. 12. MATERIAL SURDS If it is a root and irrational, it is a surd. But not all roots are surds. f a, b, (a ≠ 0 and b ≠ 0 are positive) and (m and n are real numbers) then 1. Multiplication of Surds : 1 1 1 a x b = a x b = ( a x b ) = ab 2 2 2 2. Division of Surds 1 1 a a2 a 2 a 2. a: b = = 1 =  = b b b b2
13. 13. MATERIAL SURDS 1. 2 x 18 = 36 = 6 2. 4 5 − 3 5 = 5 1 2 3 3. 3+ 3= 3= 3 2 3 3
14. 14. EVALUATION CLICK ME
15. 15. TERIMA KASIH