\[
\begin{array}{l}
 \log _4 x = \log _2 y \\ 
 \log _2 x^{\frac{1}{2}}  = \log _2 y \\ 
 x^{\frac{1}{2}}  = y \to x = y^2  \\ 
 smena\,u\,drugu:\,x^2  - 5x + 4 = 0 \\ 
 x_1  = 4 \to y_1  = 2 \\ 
 x_1  = 1 \to y_1  = 1 \\ 
 \end{array}
\]