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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        If\[\frac{\log x}{\log 5}=\frac{\log 36}{\log 6}=\frac{\log \,64}{\log y},\]what are the values of\[x\]and y respectively?

    A)  8, 25                                     

    B)  25, 8

    C)  8,8                        

    D)  25,25   

    Correct Answer: B

    Solution :

                    Now,     \[\frac{\log x}{\log 5}=\frac{\log 36}{\log 6}\] \[\Rightarrow \]               \[\frac{\log x}{\log 5}=\frac{\log {{6}^{2}}}{\log 6}=2\] \[\Rightarrow \]               \[\log x=\log 25\] \[\Rightarrow \]               \[x=25\] Again,   \[\frac{\log 36}{\log 6}=\frac{\log 64}{\log y}\] \[\Rightarrow \]               \[\frac{2\log 6}{\log 6}=\frac{\log 64}{\log y}\] \[\Rightarrow \]               \[\frac{\log 64}{\log y}=2\] \[\Rightarrow \]               \[2\log y=2\log 8\] \[\Rightarrow \]               \[y=8\]


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