no you did not solve it correctly, remember the rules of log,
is the same as
and is the same as
also
+ is the same as
and there it is, as a single logarithm, u can try to put any number back into the equation to check your working e.g. let x = 5
if u put this with x equals 5 into your calculator you will get 5.999 or something
and if you put x=5 into the single logarithm
you will get the same 5.99 so you know its correct
hope you understand