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Algebra

Blazing goIITian

 Joined: 29 Mar 2008 Post: 1024
14 Nov 2008 12:01:05 IST
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4
521
Find x
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

If  the  third term in expansion of   is 1000,then find x.......

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
14 Nov 2008 13:16:05 IST
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here the answer is x = 100;if there is ne problem in solving the question than nudge me ,i will provide you the coplete solution

Blazing goIITian

Joined: 1 Apr 2007
Posts: 1084
14 Nov 2008 13:27:09 IST
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take log [10] x = y...u wil get a quadratic in y...one root is 2..y=2..x=100..

Moderator
Joined: 16 Dec 2006
Posts: 3373
14 Nov 2008 13:29:26 IST
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5C2. (1/x)^3 ( x^[log_10 x] )^2 = 1000
(1/x)^3 ( x^[log_10 x] )^2 = 100
x^(-3) . x^(2.[log_10 x] ) = 100
x^(-3) . x^(log_10 x^2) = 100
x^[-3 + log_10 x^2] = 100
log_x 100 = -3 + log_10 x^2
3 = 2 (log_10 x - log_x 10)
take log_10 x = A, then log_x 10 = 1/A
and the result is A = 2.
So log_10 x = A = 2
x = 100

Hot goIITian

Joined: 28 Aug 2008
Posts: 162
14 Nov 2008 14:15:34 IST
2 people liked this

let   x=10^y

(10(-y)  +   10(y^2) )5

5c2 * (10(y^2) )2  * (10(-y) )    =1000

2 y2  -  3y  -2  =0

y =2,  -1/2

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