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9th Class Mathematics Related to Competitive Exam Question Bank Arithmetic

  • question_answer
    If \[{{8}^{r}}={{4}^{t}}\], then the ratio of r to t is

    A)  2: 3                         

    B)         3:2

    C)  4:3                                        

    D)  3:4

    Correct Answer: A

    Solution :

     Given,  \[{{8}^{r}}={{4}^{t}}\] \[\Rightarrow \]               \[{{({{2}^{3}})}^{r}}={{({{2}^{2}})}^{t}}\] \[\Rightarrow \]                 \[{{2}^{3r}}={{2}^{2t}}\] Now, we know that, if base is equal then powers are equal. \[\Rightarrow \]               \[3r=2t\] Thus, the ratio of \[r\] to t is \[2:3\]


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