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Nice question. I changed log 4 (x) into 1/2 log 2 (x) and log 8 (2x) into 1/3 log 2 (2x). Then found r by using 1/2 log 2 (x)*r=log 2(x), so r is 2. Using this in first two terms, 2*1/3 log 2 (2x)=1/2 log 2 (x), 1+log 2 (x) = 3/4 log 2 (x), leads to x.
