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Mathematics

If 34×93=9n3^4 \times 9^3 = 9^n, then the value of n is:

  1. 5

  2. 7

  3. 10

  4. none of the above

Exponents

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Answer

34×93=9n34×(32)3=(32)n34×36=32n34+6=32n310=32n10=2nn=102n=53^4 \times 9^3 = 9^n\\[1em] \Rightarrow 3^4 \times (3^2)^3 = (3^2)^n\\[1em] \Rightarrow 3^4 \times 3^6 = 3^{2n}\\[1em] \Rightarrow 3^{4+6} = 3^{2n}\\[1em] \Rightarrow 3^{10} = 3^{2n}\\[1em] \Rightarrow 10 = 2n\\[1em] \Rightarrow n = \dfrac{10}{2}\\[1em] \Rightarrow n = 5

Hence, option 1 is the correct option.

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