Используя свойства логарифмов, можем преобразовать уравнение:

[tex](8x) {}^{5 - 2} {}^{ log_{2}(x) } = \\frac{1}{64}[/tex]

[tex](8x)^{3log_{2}(x)} = \\frac{1}{64}[/tex]

[tex]2^{3log_{2}(8x) \\cdot log_{2}(x)} = 2^{-6}[/tex]

[tex]2^{3log_{2}(8x^2)} = \\frac{1}{64}[/tex]

[tex]2^{log_{2}(512x^6)} = \\frac{1}{64}[/tex]

[tex]512x^6 = \\frac{1}{64}[/tex]

[tex]x^6 = \\frac{1}{32768}[/tex]

[tex]x = \\sqrt[6]{\\frac{1}{32768}}[/tex]

[tex]x = \\frac{1}{8}[/tex]

Ответ: [tex]x = \\frac{1}{8}[/tex]