For the curve represented implicitly as $3^{x} - 2^{y} = 1$ , the value of $lim x \to \infty (\frac{d y}{d x})$ is

equal to

1

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equal to

0

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equal to

{log}_{2} 3

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non existent

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Solution

The correct option is C equal to ${log}_{2} 3$
$y = \frac{l o g (3^{x} - 1)}{l o g 2}$
$y^{'} = \frac{3^{x} l o g 3}{(3^{x} - 1) l o g 2}$
At $x \to \infty, \frac{3^{x}}{3^{x} - 1} \to 1$
So, $y^{'} = \frac{l o g 3}{l o g 2}$
Hence, option C is the correct option.

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