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Evaluate: lim(x->0)(3^(2x)-2^(3x))/x...

Evaluate: `lim_(x->0)(3^(2x)-2^(3x))/x`

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Verified by Experts

We have
`underset(xto0)lim(3^(2x)-2^(3x))/(x)" "`(0/0 from)
`=underset(xto0)lim{((3^(2x)-1)/(x))-((2^(3x)-1)/(x))}`
`=underset(xto0)lim((3^(2x)-1)/(2x).2)-underset(xto0)lim((2^(3x)-1)/(3x).3)`
`=2log3-3log2=log9-log8=log((9)/(8))`
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