We have two responses for you.
Hello Beth.
Let's say y = log4(x). Then 4^{y} = x. In other words, x = 2^{2y}.
Now take the log in base 2 of each side:
log_{2}(x) = log_{2} (2^{2y}) = 2y (log_{2} (2) ) = 2y = 2 log_{4}(x).
So you can substitute log_{4} (x) with (1/2) log_{2} (x).
Repeat as needed to solve for x.
Hope this helps,
Stephen La Rocque.
and
Beth,
You need to start by getting rid of the logs.
You have
256^{log256 (x) + log16 (x) + log4 (x) + log 2 (x)} = 256^{7/4}.
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
256^{log256(x)} = x, the next is 256^{log16(x)} = 16^{2log16(x)} = x^{2} and so on. You should end up with x^{13} and then you can solve for x.
Penny
