Just wondering is someone could have a look at this equation and check my answer for me?
Find the real solutions of log3(10x^2 - x - 2) = 2 + 2log3(x)
My answers came out to x = 2, -1 and I have said that x=2 is the only real solution.
In terms of my logic for why -2 is the only real solution, I came to this because I know we can't have the log of a negative number as a real solution, so 2log3(x) would mean x must be >0. Can anyone help me get a better understanding of how you should first decide what the real solutions must be and then, how to set this out on paper showing my reasoning?