logx2(81-24x) = 1; solve for x

 Ques. logx2(81-24x) = 1; solve for x.

A] x = 3 or -7 

B] x = 3 or -27 

C] x = 9 or -67 

D] x = 67 or 3

Ans - B

Solution - 

logx2(81-24x) = 1

81 – 24x = (x2)1

x2 + 24x -81 = 0

x2 + 27x – 3x – 81 = 0

x(x+27) – 3(x+27) = 0

(x+27)(x-3) = 0

x = 3 or – 27