Question
If `(9^n xx 3^5 xx (27)^3)/(3 xx (81)^4)` = 27, then the value of n is :
Answer: Option C
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`(9^n xx 3^5 xx (27)^3)/(3 xx (81)^4)` = 27 `hArr ((3^2)^n xx 3^5 xx (3^3)^3)/(3 xx (3^4)^4) = 3^3`
`hArr (3^(2n) xx 3^5 xx 3^((3xx3)))/(3 xx 3^(4 xx 4)) = 3^3 hArr (3^(2n + 5 + 9))/(3 xx 3^16) = 3^3`
`hArr (3^(2n + 14))/(3^17) = 3^3 hArr 3^(2n + 14 - 17) = 3^3`
`hArr 3^(2n - 3) = 3^3 hArr 2n - 3 = 3 hArr 2n = 6 hArr n` = 3.
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