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