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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    The number of solutions of \[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\] [IIT Screening 2001]

    A) 3

    B) 1

    C) 2

    D) 0

    Correct Answer: B

    Solution :

    \[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\] \[\Rightarrow x-1={{(x-3)}^{2}}\] \[\Rightarrow {{x}^{2}}-7x+10=0\]  \[\Rightarrow (x-5)(x-2)=0\] \[\therefore x=5,\]2 but \[x-3<0\] when \[x=2\] \[\therefore \]  only solution is \[x=5\] \[\therefore \]  Hence number of solution is one.


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