Well, maybe it's time you learn it.
It's very useful and easy to remember:
\Delta f = f'(x_0) \cdot \Delta x (*)
so the uncertainty in f is the derivative of f w.r.t. x (evaluated at the central value) times the uncertainty in x.
The justification is of course, that very close to x_0, we can approximate the function f by a straight line with slope f'(x_0). So if you vary x by an amount \Delta x, then you can approximate the change in f by the variation f'(x_0) \Delta x[/itex] of the line.<br />
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If you have multiple variables, like f(x, y, z, ...) then you can simply extend this to<br />
\Delta f^2 = \left( \frac{\partial f(x_0, y_0, z_0, \cdots)}{\partial x} \Delta x \right)^2 + \left( \frac{\partial f(x_0, y_0, z_0, \cdots)}{\partial y} \Delta y \right)^2 + \left( \frac{\partial f(x_0, y_0, z_0, \cdots)}{\partial z} \Delta z \right)^2 + \cdots<br />
which looks like a combination of that identity and the Pythagorean theorem. <br />
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[If you haven't learned about partial derivatives, forget about that last paragraph, you should remember formula (*) though].<br />
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When you apply (*) to the special case f(x) = k x^m you will get that <br />
\frac{\Delta f}{f} = m \frac{\Delta x}{x}<br />
as you said. When you apply it to f(x) = ln(x) you will get the requested answer.
