Q.

The number of integral solutions x of log(x+72)(x72x3)20 is 

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a

7

b

8

c

6

d

5

answer is C.

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Detailed Solution

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For log(x+72)   (x72x3)2to be defined x+72>0    and   x+721
    x>72>0   and  x52
Case - I : 72<x<52log(x+72)   (x72x3)20     (x72x3)21
     (x7)2(2x3)210   3x22x+40(2x3)20   3x2+2x40(2x3)20
   (3x10)  (x+4)(2x3)20  x4   or   x103    xϕ
Case - II : x>52log(x+72)  (x72x3)20   (x72x3)21          3x2+2x40(2x3)20    (3x10)  (x+4)(2x3)20  x[4,  103]  and  x52
Integral values of x{2,1,0,1,2,3}
No. of integral values of x=6

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