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evaluate:

lim x-0 [(3^2x)-(2^3x)] / x

$\lim_{x \to 0} \frac{3^{2 x} - 2^{3 x}}{x} = \lim_{x \to 0} \frac{(3^{2 x} - 1) - (2^{3 x} - 1)}{x} = \lim_{x \to 0} \frac{3^{2 x} - 1}{x} - \lim_{x \to 0} \frac{2^{3 x} - 1}{x} = 2 \lim_{x \to 0} \frac{3^{2 x} - 1}{2 x} - 3 \lim_{x \to 0} \frac{2^{3 x} - 1}{3 x} [∵ \lim_{θ \to 0} (\frac{a^{θ} - 1}{θ}) = \log a] = 2 \log 3 - 3 \log 2$

-6

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