Левая часть.
х^log₄x=?
log₄x = logₓ/logₓ4 = 1/logₓ4 = (logₓ4)⁻¹
x^(logₓ4)⁻¹ = (x^logₓ4)⁻¹ = 4⁻¹ = 1/4
правая часть.
2^(3log₄x +9) = 2^3log₄x * 2⁹= (4⁰⁾⁵)^3log₄x * 2⁹ = 4^1,5log₄x * 2⁹ =
=(4^log₄x)¹⁾⁵ * 2⁹ = x¹⁾⁵ *2⁹
само уравнение: 1/4 = х¹⁾⁵ *2⁹,
х¹⁾⁵= 1/4 : 2⁹ = 2⁻¹¹
х¹⁾⁵ = 2⁻¹¹ | ²
x³ = 2⁻²²
x = ∛2⁻²²=1/ ∛2²²= 1/128∛2