You need to learn your basic log rules:

1. log a + log b = log (ab) NOT log(a+b) which you tried to use in your second line. (Also in your first line your first + sign should be multiplication)

2. log a -log b = log(a/b)

and

3. log(a^n) = n log a

So: your first term:

(log x)(log x^2) = (log x)* 2log x = 2 (log x)^2

second term: (log x^3) = 3 log x

So you have:

2 (log x)^2 + 3 log x -5 = 0

(Hint: Think quadratic!!) and go from there.