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Evaluate lim(xrarr0)((3^(2x)-1)/(2^(3x)-...

Evaluate `lim_(xrarr0)((3^(2x)-1)/(2^(3x)-1)).`

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To evaluate the limit \( \lim_{x \to 0} \frac{3^{2x} - 1}{2^{3x} - 1} \), we can use the series expansion for \( a^x \) around \( x = 0 \). The expansion is given by: \[ a^x = 1 + x \log a + \frac{x^2 (\log a)^2}{2!} + \frac{x^3 (\log a)^3}{3!} + \ldots \] ### Step 1: Expand \( 3^{2x} \) and \( 2^{3x} \) ...
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