Basically what Cat in the Hat said. Recognise your log and exponential laws. Use them. Abuse them. Make them your friends. All of that jazz.
Also, it's worth being able to quickly identify number bases and work with them. Eg, in that question, it helps a lot to recognise that 25=5^2. If you see 27, it'll help to know that 27=3^3, and similar. You don't need to have these memorised, but you should be able to quickly do some division to see if any follow a power law like this. (eg, 27/3=9, 9/3=3, therefore 27=3*(9)=3*(3*3)=3^3).
You should also try to get everything to just one base as much as possible. Essentially have your equations in the form of, a^(f(x))=b^(g(x)). And if you get really lost, it can help to turn powers into pronumerals. Eg, let 2^x=u.
Otherwise, it's just practice, practice, practice. I think what you showed is unlikely to show up in VCAA as it's just a smidge too hard, but it'll certainly be good practice if you can do stuff with it.
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