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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    If\[y=lo{{g}^{n}}x,\]where\[lo{{g}^{n}}\]means\[log\text{ }log\text{ }log\text{ }...\](repeated n times), then \[x\text{ }log\text{ }x\text{ }lo{{g}^{2}}x\text{ }lo{{g}^{3}}x\text{ }...\text{ }lo{{g}^{n-1}}\text{ }x\text{ }lo{{g}^{n}}x\frac{dy}{dx}\] is equal to:

    A)  \[\log x\]                           

    B)  \[x\]                    

    C)  \[\frac{1}{\log x}\]         

    D)         \[1\]

    E)  \[{{\log }^{n}}x\]

    Correct Answer: E

    Solution :

    \[y={{\log }^{n}}x\] \[\therefore \] \[x\log x{{\log }^{2}}x{{\log }^{3}}x....{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\] \[=\frac{x\log x{{\log }^{2}}x{{\log }^{3}}x.....{{\log }^{n-1}}x{{\log }^{n}}x.1}{x\log x{{\log }^{2}}x{{\log }^{3}}x......{{\log }^{n-1}}x}\] \[={{\log }^{n}}x\]


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