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8th Class Mathematics Exponents and Power Question Bank Exponents and Powers

  • question_answer
    If \[{{3}^{(x-y)}}=27\] and \[{{3}^{(x+y)}}=243\], then x is equal to ____.

    A)  0                    

    B)         2                    

    C)  4                    

    D)         6

    Correct Answer: C

    Solution :

    We have, \[{{3}^{(x-y)}}=27\] or \[{{3}^{(x-y)}}={{(3)}^{3}}\] \[\therefore \] \[x-y=3\]                        ?(i) Also, \[{{3}^{(x+y)}}=243\] or \[{{3}^{(x+y)}}={{(3)}^{5}}\] \[\therefore x+y=5\]                            ?(ii) On adding (i) and (ii), we get \[2x=8\Rightarrow x=4\]


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