Ok, the original problem is as follows:

lg(3x)+lg(9x^2)

I am to simplify it. I switch it to:

lg((3x)(9x^2))

And then multiply it out to:

lg(27x^3)

Is this fully simplified? I thought it was, but my friend is saying it should be 3lg3 + 3lgx

Is this correct? Should I have cubed that 27, to 3^3, then split it back into addition form rather than multiplicative form? Seems quite round about.