When dealing with mathematics, a good point to keep in mind is that is 50% formulas, 50% proofs, and 50% imagination!
Seriously, though,first we take the formula.(X) means the current statement has a non-standard base (Not base-e or base-10), so you can't put it into a calculator. That's where this comes in. Log (X) is divided by Log b as in the original form, it is slightly lower, so must be the denominator. B also refers to base, so by all logic it must be on the bottom. d can be either of the two natural bases, but both must be the same.
For an example, this run-through from purplemath.com helps clarify how it would work.
Ok, now I understand how to do it-but I don't really get all of the reasoning behind the concept.
Hey-as the mathmatician John von Neumann said, "in Mathematics you don't understand things, you just get used to them.
If you get to a problem you can't figure, out, just write "Do it yourself", and you can then claim you you have reduced it to a problem you know how to solve, and maybe get partial marks for originality!