Using the martingale approach in the single-period binomial model, find the optimal portfolio strategy for maximizing E[log(X(1)]

Question:

Using the martingale approach in the single-period binomial model, find the optimal strategy for maximizing E[log(X(1)] and E[Xγ|(1)= γ], for γ < 1.
Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...