limn→∞ 41/n−131/n−1 is equal to - Infinity Learn by Sri Chaitanya

A
$\log_{4} 3$
B
$\log_{3} 4$
C
1
D
none of these

Solution:

We have,

$∴ lim_{n \to \infty} \frac{4^{1 / n} - 1}{3^{1 / n} - 1} = lim_{n \to \infty} \frac{\frac{4^{1 / n} - 1}{1 / n}}{{(\frac{3^{1 / n} - 1}{1 / n})}^{}} = \frac{\log_{e} 4}{\log_{e} 3} = \log_{3} 4$

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