First slide

Introduction to limits

Question

$lim_{n \to \infty} \frac{4^{1 / n} - 1}{3^{1 / n} - 1}$ is equal to

Moderate

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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