What is the number of solutions of log₄(x – 1) = log₂(x – 3)?

log₄(x–1) = log₂(x–3) gives (1/2)log₂(x–1) = log₂(x–3), so log₂(x–1) = 2 log₂(x–3) = log₂(x–3)². Hence x–1 = (x–3)², giving x–1 = x² – 6x + 9, so x² – 7x + 10 = 0, yielding x = 2 or x = 5. For x = 2, x – 3 = –1 < 0 (invalid for log). Only x = 5 is valid. So there is exactly one solution.