Could you give detailed solution

Question 3. Suppose my utility function for my asset position x is given by u(x)= ln(x+10). I have $4,000 at present. Consider the following lottery: L : With probability 0.3 , L yields a payoff of $1,400, and with probability 0.7 , L yields a payoff of $200 (a) If I don't have the right to play L, find an equation that when solved would yield the amount I would be willing to pay for the right to play L. This is called the buying price of lottery L. (b) If I have the right to play L, what is the least I would accept from somebody who wanted to buy the right to play L? (After someone else buys L, I cannot play L.) This is called the selling price of lottery L. (c) Find a utility function for my asset position x,u(x), such that for all possible asset positions, the buying price of L and the selling price of L will remain the same, and the buying price of L will equal the selling price of L