First slide

Introduction to limits

Question

$lim_{x \to 1} {(\log_{2} 2 x)}^{\log_{x} 5}$ is equal to

NA

A

$\log_{2} 5$
B

$e^{\log_{2} 5}$
C

e
D

0

Solution

$\begin{matrix} lim_{x \to 1} {(\log_{2} 2 x)}^{\log_{x} 5} = lim_{x \to 1} {(\log_{2} 2 + \log_{2} x)}^{\log_{x} 5} \\ = lim_{x \to 1} {[{(1 + \log_{2} x)}^{\frac{1}{\log_{2} x}}]}^{\log_{2} {xlog}_{x} 5} \\ = e^{lim_{x \to 1} \log_{2} 5} = e^{\log_{2} 5} \end{matrix}$

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