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9th Class Mathematics Number System and its Operations Question Bank Number Systems

  • question_answer
    The value of \[x,\]if \[{{5}^{x-3}}{{.3}^{2x-8}}=225\] is______.

    A)  3                                

    B)  4        

    C)  2                    

    D)         5        

    Correct Answer: D

    Solution :

    We have, \[{{5}^{x-3}}{{.3}^{2x-8}}=225\] \[\Rightarrow \]\[\frac{{{5}^{x}}}{{{5}^{3}}}.\frac{{{3}^{2x}}}{{{3}^{8}}}={{(15)}^{2}}\] \[\Rightarrow \]\[{{5}^{x}}{{.3}^{2x}}={{5}^{2}}\times {{3}^{2}}\times {{5}^{3}}\times {{3}^{8}}\] \[\Rightarrow \]\[{{5}^{x}}{{.3}^{2x}}={{5}^{5}}\times {{3}^{10}}\] On comparing, we get \[x=5\]


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