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Question

If logx3(x210x+24)logx3(x26), then
 
 
  1. x(6,4)
  2. x(6,3)
  3. x(6,6) 
  4. x(3,4)


Solution

The correct option is D x(3,4)
logx3(x210x+24)logx3(x26)
log function is defined when
(i) x210x+24>0
(ii) x26>0
(iii) x3>0  and  x31

(i)(x4)(x6)>0
x(,4)(6,)   (1)

(ii) x26>0
x(,6)(6,)   (2)

(iii)x(3,){4}   (3) 

Now, (1)(2)(3) will give
x(3,4)(6,)   (4)

Case 1: x3>1x>4
logx3(x210x+24)logx3(x26)
(x210x+24)(x26)
x3
which is not possible as x>4

Case 2: 0<x3<1x(3,4)   (5)
logx3(x210x+24)logx3(x26)
(x210x+24)(x26)
x3   (6) 
From (5) and (6)
x(3,4)   (7)

From (4) and (7)
x(3,4)

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