Using the substitution method, help me prove that . I am looking to find constants c and n0. This is what I have so far (and not sure if it is correct):

//Ignore the floor because it just ensures that the n is an integer (assuming it doesn't matter asymptotically)

//Distribute c

//rewrite lg(n+6/2) to lg(n+6) - lg(2) --> lg(2) evaluates to 1

I understand the goal is to inductively prove that T(n) is less than or equal to cnlgn but I am not quite sure how to do that at this point.