For problem two: I got to the answer by substituting a = 0.2^3 if you try that, you'll get two roots with the same things inside, leading you to compare only the root exponents

For problem 3: you're on the right track, just change the base of the logarithm on the left hand side by remembering ln(x) =log 3 (x)/log 3(e). From there, you just need to isolate all the x on one side, the log 3(e) on the other, and do 3 to the power of that to get just x on the left-hand side. Then you can use that property of logarithms on the right hand side to get all the log 3(e) in terms of ln(3) and simplify some more.