What is the derivative of log x-2?

The formula for finding the derivative of a log function of any "a" base is

(dy/dx)log base a (x) = 1/((x)ln(a))

If we're talking about base "e" (natural logs) the answer is 1/(x-2)

I think you're asking for the derivative of y = logx2. It's (-logx2)/(x(lnx)).