Step 1 :Combine the two logarithms on the left side of the equation into a single logarithm using the property of logarithms: \(\log_b(a) + \log_b(c) = \log_b(ac)\). This gives us \(\log_9(x(8x - 1)) = 1\).
Step 2 :Rewrite the equation in exponential form to remove the logarithm using the property: \(\log_b(a) = c\) is equivalent to \(b^c = a\). This gives us the final equation without logarithms: \(\boxed{9^1 = x(8x - 1)}\).