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Well I'm not actually sure what you mean by inverse, what are trying to do with it, or why it would help you get f'(x). You are however correct that x = log(base 3)(k), but I would say that should be obvious from the initial problem, as it is basically the definition of a logarithm.
Here is how I would figure out f'(x) and f''(x):
f(x) = 3^x
f(x) = e^(x * ln(3))
f'(x) = d(e^(x * ln(3)))/dx
f'(x) = e^(x * ln(3)) * ln(3)
f'(x) = 3^x * ln(3)
f''(x) = d(3^x * ln(3))/dx
f''(x) = d(e^(x * ln(3)) * ln(3))/dx
f''(x) = ln(3) * d(e^(x * ln(3)))/dx
f''(x) = ln(3) * ln(3) * 3^x
[ 06-04-2005, 01:58 AM: Message edited by: Seraph ]
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