Question:

Notice that the cleanest route is to simplify the structure before computing. A clever move here is to translate the logarithmic statement into a friendlier algebraic form. Convert log_4 into base 2 and use x > 3. The equation becomes (1/2)log_2(x - 1) = log_2(x - 3), so log_2(x - 1) = log_2((x - 3)^2). Hence x - 1 = (x - 3)^2. Solving gives x = 1 or 6, and only x = 6 satisfies x > 3. So there is exactly one solution. Trap: Apply the domain restriction x > 3 at the end. Now, we invoke the power of the relevant logarithmic identity, simplify carefully, and finally verify the domain so that no extraneous answer survives.