Question

Find n ↑

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Answer 1

Solution:-Can be solved by using the formula of limit,but we will try Simple method of L'Hopital rule

$lim(x = > 2) \frac{ {x}^{n} - {2}^{n} }{x - 2} \\ diffrentiate \: the \: term \: with \: respect \: to \: x \\ lim(x = > 2) = \frac{n {x}^{n - 1} - 0}{1 - 0} \\ now \: eqaute \: it \: to \: 80 \\ \frac{n {x}^{n - 1} }{1} = 80 \\ n \times {x}^{n - 1} = 5 \times 16 \\ n \times {x}^{n - 1} = 5 \times {2}^{5 - 1} \\ comparing \: both \: side \: we \: get \\ n = 5$

Answer 2

Answer:

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