First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{4^{x} - 1}{3^{x} - 1}$ equals

Moderate

A

$\log_{3} 4$
B

$\log_{4} 3$
C

$\log_{e} 4$
D

1

Solution

We have,
$lim_{x \to 0} \frac{4^{x} - 1}{3^{x} - 1} = lim_{x \to 0} \frac{4^{x} - 1}{x} \times \frac{x}{3^{x} - 1} = \frac{\log_{e} 4}{\log_{e} 3} = \log_{3} 4$

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