Consider different prior probs: in particular assign to ln(2x) probability 1/2 and to ln(x/2) probability 1/2. Then, the expected value of the other envelop becomes
ln(2x) 1/2 + ln(x/2) 1/2 = ln(x)
which is the same as the logarithm of the value on your envelop.

## Consider different prior

Consider different prior probs: in particular assign to ln(2x) probability 1/2 and to ln(x/2) probability 1/2. Then, the expected value of the other envelop becomes

ln(2x) 1/2 + ln(x/2) 1/2 = ln(x)

which is the same as the logarithm of the value on your envelop.