MathematicsIf a= 2 x−1 2 x−2 ,b= 2 −x 2 x+1   and a−b=0  . Then, which of the following is the value of x?

If a= 2 x1 2 x2 ,b= 2 x 2 x+1   and ab=0  . Then, which of the following is the value of x?


  1. A
    1
  2. B
    0
  3. C
    1  
  4. D
    None of these 

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    Solution:

    Given that a= 2 x1 2 x2 ,b= 2 x 2 x+1   and ab=0  .
    Substitute a and b in ab=0  ,
    ab =0 2 x1 2 x2 2 x 2 x+1 =0 2 (x+1) 2 x1 2 x2 2 x 2 x2 2 x+1 =0  
    Applying a p × a q = a p+q  ,
    Comparing the exponents, we get,
    2x=2 x=1  
    Hence, the value of x is 1  .
    Therefore, option 3 is correct.
     
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