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.
Thanks heaps—managed to get them both! It's good to know I wasn't too far off. I had a feeling I needed to do change of base but I wasn't exactly sure where I needed to go with it.
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.
Thanks heaps—managed to get them both! It's good to know I wasn't too far off. I had a feeling I needed to do change of base but I wasn't exactly sure where I needed to go with it.