Why do we determine the values of λ in regularization as ln λ, such as ln λ=-18 instead of for example λ=0.3?
I can just suppose, that it's because then we could consider regularization together with a Log Likelihood function, for instance, and that is why it's more convenient to have such a representation. It's easier to make computations, using log, for example, when we want to minimize some functions (ln a + ln b = ln(a*b), (ln a)' = 1/a etc)