Решить уравнение [latex](log_{x}(2))(log_{x/16}(2))=log_{x/64}(2)[/latex]

[latex](log_{x}2)(log_{ \frac{x}{16}}2)=log_{ \frac{x}{64} }2 \\\ x>0;x \neq 1;x \neq 16;x \neq 64 \\\ \cfrac{1}{log_{2}x} \cdot \cfrac{1}{log_{2} \frac{x}{16}} =\cfrac{1}{log_{2} \frac{x}{64}} \\\ \frac{1}{log_{2}x} \cdot \frac{1}{log_{2}-log_{2}16} =\frac{1}{log_{2}-log_{2}64} \\\ \frac{1}{log_{2}x} \cdot \frac{1}{log_{2}-4} =\frac{1}{log_{2}-6} [/latex] [latex]log_{2}x=a \\\ \frac{1}{a} \cdot \frac{1}{a-4} =\frac{1}{a-6} \\\ \frac{1}{a(a-4)} =\frac{1}{a-6} \\\ a(a-4)=a-6 \\\ a^2-4a-a+6=0 \\\ a^2-5a+6=0 \\\ (a-2)(a-3)=0 \\\ a_1=2 \\\ log_{2}x_1=2 \\\ x_1=2^2=4 \\\ a_2=3 \\\ log_{2}x_2=3 \\\ x_2=2^3=8[/latex] Ответ: 4; 8