1. INDICES, SURD
AND LOGARITHM
LYDIA VALENSIA
Email : lydia.valensia@yahoo.com SMA NEGERI 2 SEKAYU

2. INTRODUCTION LET’S EXPLORE
“INDICES, SURDS AND LOGARITHM”
COMPETENCES
INDICATOR
MATERIAL
EVALUATION

3. INTRODUCTION
Are you smarter than 9th
grader?
COMPETENCES
INDICATOR
DO YOU KNOW ?
MATERIAL
EVALUATION

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. 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. INTRODUCTION
COMPETENCES
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. INTRODUCTION
COMPETENCES
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. 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. 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. 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. 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. 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. 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. EVALUATION
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15. TERIMA KASIH