First, because of the logs, we must have both x+1 and x-1 positive. Also, I am reading log2(stuff) as log (base 2) of stuff. Second, 8 = log2(2^8), so we have

log2(x+1) = log2( 2^8 / (x-1) )

so

x+1 = 2^8 / (x-1)

(x+1)*(x-1) = 2^8

x^2 -1 = 256

x^2 = 257

x = +sqrt(257) since we cannot have x-1 negative.

-- Professor Jeff Stuart, Chair Department of Mathematics Pacific Lutheran University jeffrey.stuart@plu.edu (253) 535 7403