Question about logarithms

Hi Guys,

I having some trouble with logarithms again. I am able to solve them okay most of the time. But my final answer answer doesn't match the given one.

Take the following problem for instance. I solved upto

The required answer is,

In this case I see that I could get to the required answer by going flipping the base, 4^1/2 and so on.

In this example I am close to the final answer, but many times I am not this close. Is there a general rule to follow when simplifying? How do I figure out what base the answer should be in? Where should the simplification end?