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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    The number of solutions of\[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\]is/ are

    A)  0                                            

    B)  1

    C)  2                            

    D)         3

    Correct Answer: B

    Solution :

    Given that,\[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\] \[\therefore \]  \[x-1={{(x-3)}^{2}}\] \[\Rightarrow \]               \[{{x}^{2}}-7x+10=0\] \[\Rightarrow \]               \[(x-5)(x-2)=0\] \[\Rightarrow \]               \[x=2,\,\,5\] \[\Rightarrow \]\[x=5\], but\[x=2{{\log }_{2}}(x-3)\]is not satisfied.


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