Verified answer

Is it: 8^(x*2) = 4x - 1 ?

Ok, you can bring down that exponent by taking the log of both sides:

ln(8^(x*2)) = ln(4x - 1)

(x*2)*ln(8) = ln(4x - 1)

x*2 = ln(4x - 1) / ln(8)

x = ln(4x - 1) / (2*ln(8))