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Question Number 12279 by chux last updated on 17/Apr/17

i guess i posted this question but

didnt really get much response .

pls help out

if {8 \log}_{2} x + (x - 1) \log_{x} 2 = 3^{x}

find x .

Commented by mrW1 last updated on 17/Apr/17

t h e r e i s n o a n a l y t i c a l s o l u t i o n f o r

s u c h e q u a t i o n . b y t r i a l a n d e r r o r y o u

c a n s e e t h a t x = 2 i s a s o l u t i o n . u s i n g

g r a p h i c a l m e t h o d y o u c a n f i n d t h e

o t h e r s o l u t i o n x \approx 1.3853 .

Commented by mrW1 last updated on 18/Apr/17

t h e newton raphson iteration t o s o l v e

f (x) = 0 i s :

i f y o u h a v e a s t a r t v a l u e x_{0} f o r t h e s o l u t i o n,

y o u c a n g e t a b e t t e r v a l u e w i t h

x_{n + 1} = x_{n} - \frac{f (x_{n})}{f^{'} (x_{n})} (n = 1, 2, 3 \dots .)

y o u r e p e a t t h i s t i l l x_{n + 1} - x_{n} i s s m a l l

e n o u g h f o r y o u .

y o u r c a s e i s n o t g o o d f o r d e m o n s t r a t i o n .

l e t u s s e e f (x) = \sin x - 0.4 = 0

f^{'} (x) = \cos x

x_{0} = 0.4

x_{1} = 0.4 - \frac{\sin 0.4 - 0.4}{\cos 0.4} = 0.411488553

x_{2} = 0.411488553 - \frac{\sin 0.411488553 - 0.4}{\cos 0.411488553} = 0.411516846

x_{3} = \dots . = 0.411516846 \approx x_{2}

w e g e t a f t e r 3 i t e r a t i o n s a g o o d s o l u t i o n

f o r \sin x - 0.4 = 0 :

x \approx 0.411516846

Commented by chux last updated on 18/Apr/17

thanks sir \dots . . a friend told me about

a method called newton raphson

iteration but i dnt knw how it can

be applied \dots . please can you

explain the method and applicatn

to thiz question if possible \dots .

thanx for always helping .

Commented by chux last updated on 18/Apr/17

thanks boss

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