Suci Wulandari – Hi Welcome to my blog. Hope you enjoy it

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II .Algebraic Forms and Processes

: I T R A

P Powers ,Roots ,and Logarithms s

d r o

W Pronunciation Indonesian

e w o

P r s _{/ a'p ʊə( / r)z} Bliangan Berpangkat s

e c i d n

I /’næt∫ra l’nΛmbə( z/ r) Bliangan Asil e

s a

B _{/beɪs /} Bliangan Pokok

s i s a

B _{/' eb ɪs}əs / Bliangan Pokok

t n e n o p x

E _{/ɪk' ps əʊnən / t} Pangkat

s t o o

R /ru:tz/ Bentuk Akar

s l a c i d a

R _{/rædɪk z/ l} Bentuk Akar

Radica lsign _{/ dræ ɪk z al s ɪn/} Tanda Akar d

n a c i d a

R _{/rædɪkən /} Bliangan yang diakarkan e

r a u q s t c e f r e

P _{/ p’ ɜf:ɪkt skwe}ə( / r) Kuadrat Sempurna l

a i m o n i

B _{/baɪ'nəʊmɪəl/} Binomial

e t a g u j n o

C _{/'kɒndƷʊgeɪt /} Sekawan

m h t i r a g o

L _{/'lɒgəriðəm /} Logaritma

Example:

• Powersori ndices is used when wewant to multiplya number by i tsel f .

s e m i t l a r e v e s

• I xn n _{rte m ,x iscalledbase or basis and n is ca lled exponent.}

• Root isi nversiono fexponentiation.

• n_{a is called radica lexpression (or radica lform) because it contains a} .

t o o r

• In3_a+_{b , +a bi sthe radicand ,and 3 i sthe index.} • Anumberi ssaid perfectsquare fi i tsrootsarei ntegers.

• Numbers such as 9 ,16 ,36 ,and 100 are perfect squares ,but 12 and 20 .

t o n e r a

• The square root is in simplest form fi the radicand does not contain 1

n a h t r e h t o s e r a u q s t c e f r e

p ,no fraction is contained in radicand ,and o

n radicalsappear i nthedenominator o fa f raction.

• Aradica landa number i sca lled a binomial.

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s

r e w o P y a S o t w o

H ,Roots ,andLogarithms

x2 _{• xsquared /'skweə(r)d/}

x3 _{• xcubed /kju:bd/}

xn _{• xto the power o fn}

• xto the n-th power

• xto the n

• xto the n- ht

• xupper n

• xraisedbyn

/' pΛ ə(r)/ / d z i e r /

) y + x

( 2 _{• xplus yal lsquared}

• bracketx plus ybracket closed squared

• xplus yi n bracket squared

/'brækit/

x • squareroot o fx • root o fx

3_{y • cube root o fy}

n_{z • n-throot o fz}

3 2

5_{x y} • ffithroot of ( pause )x squared times ycubed

• ffithroot o fx squared times ycubed i nbracket n_{logx • log x to the baseo fn}

• log basen o fx

l /ɒg /

2 n

l • naturall ogo ftwo

• “L N” o ftwo

5_log2 _{52 • log squared o ftwenty-ifve to the baseo f ifve}

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M ro e Examples

2_{log ( x+y)+2} 2_{log 4x >4} log base t woof xplusyi n bracke tplust wo itmes r

u o f n a h t r e t a e r g s i s ’ x r u o f f o o w t e s a b g o l

s l a u q e x f o t o o r r e v o e n o ) e s u a p ( s u l p d e r a u q s x

e n o

s u n i m x r e p p u e n i n ) e s u a p ( s u l p x r e p p u e e r h t

y t n e w t n a h t e r o m s i ) e s u a p ( e n

o -seven

o w t n a h t s s e l s i e n o s u n i m ) e s u a p ( x e h t o t e n i n

e c i t c a r P

.

1 Read out thef ollowing terms. .

a 26

.

b 2 3

3

    

.

c x5 _{x :} 2_=x3 .

d (3ab)4

. e

3 x

y 3

 

 

 

.f (9x)0

.

g 4x4

.

h 4_m3_n8 m = 3/4_n2

.i 5 3a =a3/5

.j 3_8x6_y9

.

k _x2 +_y2 .l ax_{l go b}

. m log a2

.

n 2_{log ( 1/6)} .

o 5_{log ( x}2_{+ y )} .

p (n_{log x)}2 .

q 6_log2 _{2 – 2} 6_logx2 _-1

2 1 ₁

x

x =

+

1 x

x _{9 27}

3 ₊ − _>

x _{1 2}

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.

2 Read theseexpressions and simplfiythem. .

a 53_×513 .

b 814 _:811

.

c

( )

24 3

. d

2 7

3 x x

 

  _  _ 

.

e 2431/5 .f -4-2

.

g 1251/3 .

h (- )5-1 .i 3-3 .j 7 2

.

k 234

.l 5 3 2+

.

m 3

2 6−

: I I T R A

P Algebraic Process

s d r o

W Pronunciation Indonesian

d n a p x

E / ɪk p’ æ /s n d Uraikan/Jabarkan Simplfiy /’sɪmplɪfaɪ/ Sederhanakan

e z i r o t c a

F / fæ t’ k əraɪz/ Faktorkan

l e c n a

C / k’ æ ln / s Coret/Hapus/Batalkan b

u

S stitute / s’ Λ tbs ɪtju:t/ S sub titusi e

d i

S / as ɪd/ Ruas

t f e

L -hand side /left hæn d as ɪd/ Ruaskiri t

h g i

R -handside / ar ɪt æn h d as ɪd/ Ruaskanan t

c e ll o

C /kə’lək / t Kumpulkan

e t a n i m il

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Examples:

.

1 Expand ( x-3 ()x+2)i nto x2_{-x- .6} .

2 Simplfiythel eft handside( LHS )o fequation(2x+2()xy+y )=5y i nto y 5 = ) 1 + x ( y 2 .

3 Factorizex3_{- x2} 2_{+ -3x 2 i nto ( -x 1()x+1 ()x- )2} .

4 Cancel( x+1)f rom 2( +x 1)/(x+1 )to get 2 .

5 Multiplybothsideo fequation ½x =4 with2 to getx=8 .

6 S sub titute y=4 i ntoequation2x+y=12 and wehave2x+4=12 .

7 Co llect( x+2)f rom ( x+2)3_{-2(x+2()x+1 )toget( x+2)([x+2)}2_-2(x+1])

x

E ample

d n i

F x thatsatisfyequation 3x-3x-1=162. r e w s n A . 3 e v a h e w d n a , 3 h t i w e d i s h t o b y l p i t l u m e w , t s r i

F 3x-3x=486.

t c e ll o c e w , n e h

T 3x ,and we g 3x 3et ( -1)=486 ,which can be simp ilifed

. 2 o t n

i 3x=486.

t e g e w , 2 y b e d i s h t o b e d i v i

D 3x=243 .

n o r e b m u n t a h t w o n k e

W theright hand side( RHS )equals35 ,so wecan

3 e t i r

w x 3= 5 .

. 5 o t l a u q e e b t s u m x , s r e w o p f o e l u r e h t o t g n i d r o c c A e s i c r e x E . w o l e b s m e l b o r p f o n o i t u l o s e h t d n if o t s s e c o r p e h t n i a l p x E f o m e t s y s r o , y t il a u q e n i , n o i t a u q e h c a e s e if s i t a s t a h t x d n i

F equations.

.

1 1 – 4x≤x+11

. 2

2 3 y-

3 5 =