Conditional expectation of a geometric Brownian motion with a power?

Question

Let $X_T$ satisfies a time-dependent geometric Brownian motion: $$ \frac{d X_s}{X_s}= \mu_s ds+\sigma_s dB_s,~t\leq s\leq T. $$

Could I write a conditional expectation of $X_T^\gamma$ in the following form: $$ {\rm E}_t[X_T^{\gamma}]={\rm exp}\left({\rm E}_t[\log X_T^\gamma]+\frac12{\rm Var}_t(\log X_T^\gamma)\right)~??? $$

Thank you very much!