Step 1: Identify the mathematical form.
The given equation is \[ E = K_k \ln \frac{d_1}{d_2} \] where \(E\) is the energy for size reduction, \(d_1\) is the starting particle size, and \(d_2\) is the final particle size, connected through a natural logarithm.
Step 2: Compare against the standard size reduction laws.
Rittinger's law uses reciprocal diameters, \(E = K_R (1/d_2 - 1/d_1)\), and Bond's law uses reciprocal square roots, \(E = K_B (1/\sqrt{d_2} - 1/\sqrt{d_1})\). Neither contains a logarithm, so both are ruled out by form alone.
Step 3: Match to Kick's law.
Kick's law is defined exactly as \[ E = K_k \ln \frac{d_1}{d_2} \] stating that the energy needed depends on the logarithm of the size reduction ratio, which is identical to the equation given in the question.
Step 4: Final Answer.
\[ \boxed{\text{Kick's law}} \]