$d$-Dimensional Brownian Motion Martingales

Let $d > 1$ and let $W_t$ denote a standard $d$-dimensional Brownian motion starting at $x\neq 0$. Let $M_t = \log|W_t|$ for $d = 2$, and $M_t= |W_t|^{2-d}$ for $d > 2$. Show that $M_t$ is a martingale.

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@ user : Use Itô's lemma and look at the drift part and check that the diffusion part is ok for your process to be a martingale and not only a local martingale. Best regards –  TheBridge Mar 30 '12 at 13:19