Решите уравненияlog0,5 x + 3 logx 0,5 = 45 log3 x - 3 logx 3 = 2log0,3 x + 9 logx 0,3 = 10

1)  log₀.₅X + 3* [latex] \frac{ log_{0.5}0.5 }{ log_{0.5}X } [/latex] = 4    log₀.₅² X + 3 = 4log₀.₅X log₀.₅X = t t² - 4t + 3 =0 t₁ = 1 t₂ = 3 log₀.₅X = 1 x = 0.5 log₀.₅X = 3 x = 0.125 Ответ: 0,5; 0,125 2) 5*log₃X - 3*[latex] \frac{ log_{3}3 }{ log_{3}X } [/latex] = 2    5*log₃²X - 3 = 2log₃X log₃X = t 5t² - 2t - 3=0 t₁ = 1 t₂ = [latex]- \frac{3}{5} [/latex] log₃X = 1 x = 3 log₃X= [latex]- \frac{3}{5} [/latex] x= [latex] 3^{- \frac{3}{5} } = \frac{1}{ \sqrt[5]{27} } [/latex] 3) log₀.₃X + 9*[latex] \frac{ log_{0.3}0.3 }{ log_{0.3}X } [/latex] = 10 log₀.₃²X + 9 = 10*log₀.₃X log₀.₃X = t t² - 10t + 9=0 t₁ = 1 t₂ = 9 log₀.₃X = 1 x = 0.3 log₀.₃X = 9 x = (0.3)⁹