CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007

  • question_answer
    If\[{{\log }_{\sqrt{3}}}5=a\]and\[{{\log }_{\sqrt{3}}}2=b,\]then \[{{\log }_{\sqrt{3}}}300\]is equal to

    A)  \[2(a+b)\]                         

    B)  \[2(a+b+1)\]

    C)  \[2(a+b+2)\]    

    D)         \[a+b+4\]

    E)  \[a+b+1\]

    Correct Answer: B

    Solution :

    Given that, \[{{\log }_{\sqrt{3}}}=5a\]and \[{{\log }_{\sqrt{3}}}2=b\] \[\therefore \] \[{{\log }_{\sqrt{3}}}300={{\log }_{\sqrt{3}}}3+{{\log }_{\sqrt{3}}}100\]                 \[=2{{\log }_{\sqrt{3}}}\sqrt{3}+2{{\log }_{\sqrt{3}}}5+2{{\log }_{\sqrt{3}}}2\] \[=2(1+a+b)\]


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