We have two responses for you.
Let's say y = log4(x). Then 4y = x. In other words, x = 22y.
Now take the log in base 2 of each side:
log2(x) = log2 (22y) = 2y (log2 (2) ) = 2y = 2 log4(x).
So you can substitute log4 (x) with (1/2) log2 (x).
Repeat as needed to solve for x.
Hope this helps,
Stephen La Rocque.
You need to start by getting rid of the logs.
256log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 2567/4.
Simplify the right hand side by first taking a 4th root. As for the left hand side, since the bases involved are powers of 2, you can break it into a product of 4 parts, the first of which is
256log256(x) = x, the next is 256log16(x) = 162log16(x) = x2 and so on. You should end up with x13 and then you can solve for x.