4. In $\triangle A B C$, the sides opposite to angles $A, B, C$ are denoted as $a, b, c (b \neq 1)$, respectively, and $\frac{C}{A}, \frac{\sin B}{\sin A}$ are both roots of the equation $\log _{\sqrt{6}} x=\log _{6}(4 x-4)$. Then $\triangle A B C$
(A) is an isosceles triangle, but not a right triangle;
(B) is a right triangle, but not an isosceles triangle;
(C) is an isosceles right triangle;
(D) is neither an isosceles triangle nor a right triangle.