To solve this equation, we need to convert both sides to exponential form.

For the left side:
log^4 (2-x) = log(2-x) / log(4)

For the right side:
log^16 25 = log(25) / log(16)

Next, set the left and right sides equal to each other and solve for x:

log(2-x) / log(4) = log(25) / log(16)

log(2-x) / log(4) = log(25) / log(16)

Cross multiply to get:
log(2-x) log(16) = log(25) log(4)

Convert both sides to exponential form:
16^(log(2-x)) = 25^(log(4))

Now solve for x.