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Q.

$\underset{x \to 0}{L t} \frac{6^{x} - 3^{x} - 2^{x} + 1}{x^{2}}$

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a

$({\log_{e}}^{2}) ({\log_{e}}^{3})$

b

log_e⁵

c

log_e⁶

d

0

answer is A.

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Detailed Solution

$\begin{array}{l} \underset{x \to 0}{L t} \frac{6^{x} - 3^{x} - 2^{x} + 1}{x^{2}} = \underset{x \to 0}{L t} \frac{3^{x} {.2}^{x} - 3^{x} - 2^{x} + 1}{x^{2}} \\ \underset{x \to 0}{L t} \frac{(3^{x} - 1)}{x} \frac{(2^{x} - 1)}{x} = (\log_{e}^{3}) (\log_{e}^{2}) \end{array}$

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