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If lim(x to 3) (x^(n) - 3^(n))/(x - 3) ...

If `lim_(x to 3) (x^(n) - 3^(n))/(x - 3) = 1458` and `n in N`, find n.

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We have `underset(x to 3)(lim) (x^(n) - 3^(n))/(x - 3) = 1458`
`implies n.3^(n - 1) = 1458`
`implies n.3^(n - 1) = 6(3)^(6 - 1)`
`implies n = 6`
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