${\log _4}(x - 1) = {\log _2}(x - 3)$ $\Rightarrow {1 \over 2}{\log _2}(x - 1) = {\log _2}(x - 3)$ $\Rightarrow {\log _2}{(x - 1)^{1/2}} = {\log _2}(x - 3)$ $\Rightarrow {(x - 1)^{1/2}} = {\log _2}(x - 3)$ $\Rightarrow {(x - 1)^{1/2}} = x - 3$ $\Rightarrow x - 1 = {x^2} + 9 - 6x$ $\Rightarrow {x^2} - 7x + 10 = 0$ $\Rightarrow (x - 2)(x - 5) = 0$ $\Rightarrow x = 2,5$ But x $\ne$ 2 because it is not satisfying the domain of given equation i.e. log 2 (x $-$ 3) $\to$ its domain x > 3 finally x is 5 $\therefore$ No. of solutions = 1.