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

  • question_answer
    If \[\frac{10}{3}\times {{3}^{x}}-{{3}^{x-1}}=81\], then the value of x is____.

    A)  2                                

    B)  1        

    C)  3                    

    D)         0        

    Correct Answer: C

    Solution :

    We have, \[\frac{10}{3}\times {{3}^{x}}-{{3}^{x-1}}=81\] \[\Rightarrow 10\times {{3}^{x-1}}-{{3}^{x-1}}=81\] \[\Rightarrow {{3}^{x-1}}(10-1)=81\Rightarrow {{3}^{x-1}}=81\] \[\Rightarrow {{3}^{x-1}}=\frac{81}{9}=9\Rightarrow {{3}^{x-1}}={{3}^{2}}\] On comparing, we get \[x-1=2\Rightarrow x=2+1=3\]


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