So im having a problem with the following:

Show that $\lceil lg(x+1)\rceil = \lfloor lg x \rfloor +1$ for integers $x\ge 1$.

I started to show it by proving by induction, only problem was after showing x=1 holds true, then assuming x=n work, i went to the final step of trying to do $x=n+1$ and got stuck. Im not sure if im just simplifying it wrong or what but I cant seem to get it in any forms that are noticeably correct.