lim-x-log-x-2021x-log-x-pi-iberty-

Question Number 129655 by liberty last updated on 17/Jan/21

\lim_{x \to \infty} {(\log_{x} (2021 x))}^{\log x} = ?

⌈ * ⌉ (\sqrt{π^{ℓ iberty}})

Answered by bemath last updated on 17/Jan/21

\lim_{x \to \infty} {(\frac{\ln (2021 x)}{\ln x})}^{\ln x} = \lim_{x \to \infty} {(1 + \frac{\ln 2021}{\ln x})}^{\ln x}

\lim_{x \to \infty} {[(1 + \frac{1}{(\frac{\ln x}{\ln 2021})}) \frac{\ln x}{\ln 2021}]}^{\ln 2021} = e^{\ln 2021} = 2021

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