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Question

The solution set of log1/3(2x+24x)2, is 
  1. (,213)
  2. (,2+13)
  3. (,2)
  4. R


Solution

The correct option is C (,2)
log1/3(2x+24x) is defined, if 
2x+24x>0
4(2x)(2x)2>0
2x(42x)>0
42x>02x<4x<2x(,2)...(1)

We have , 
 log1/3(2x+24x)2
(2x+24x)(13)2
2x+2(2x)29
4(2x)(2x)290
(2x)24(2x)+90
(2x2)2+50
Which is true for all xR...(2)

From (1) & (2)
x(,2).

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