If your professor gives you a function that is not a standard "memorize how to take the derivative" function, assume that he made a mistake, forget that dy/dx of log x is not the same as dy/dx lnx and don't waste 40+ minutes trying to find a way around taking the derivative of the function.
In case you're curious, log x = lnx/log (base), so the derivative of logx = 1/log(base) * x. As it turns out, in the problem you end up dividing two derivitaves of a log by each other, so the log(base) drops out, and you're left with the same exact thing as if they were lnx.
And yes, I realize not everybody is going to know what I'm talking about, but some of you will, and that's all that matters.
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