MathematicsFind the value of x , where x is an integer  



Find the value of x , where x is an integer
 


  1. A
    2
  2. B
    4
  3. C
    9
  4. D
    13
     

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    Solution:

    We have to find the value of x in  . Let us simplify this equation.
    We know that  . Hence, we can write the above equation as

    Now, we can write 8 in terms of power as  . Hence,

    We know that . Hence, the above equation can be written as

    Now, let us take  outside the numerator. We will get

    We can write this as

    Let us cancel the common factors from numerator and denominator. We will get

    Let us take the denominator to the RHS. We will get

    We can now solve the RHS by cancelling the common factors.

    Now, let us write 8 in terms of powers of 2. We will get

    We know that . Hence, we can write the above expression as

    We have studied that . So the above expression becomes

    We know that if the bases are equal on both the sides, then their powers are equal. Hence,

    By solving this, we will get
    x = 4
    Hence the value of x is 4.
    So, the correct Ans is “Option 2”.
     
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