Ответы и объяснения

2014-01-15T17:11:34+04:00
1)  log₀.₅X + 3*  \frac{ log_{0.5}0.5 }{ log_{0.5}X } = 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* \frac{ log_{3}3 }{ log_{3}X } = 2
   5*log₃²X - 3 = 2log₃X
log₃X = t
5t² - 2t - 3=0
t₁ = 1
t₂ = - \frac{3}{5}

log₃X = 1
x = 3
log₃X= - \frac{3}{5}
x=  3^{- \frac{3}{5} } =  \frac{1}{ \sqrt[5]{27} }

3) log₀.₃X + 9* \frac{ log_{0.3}0.3 }{ log_{0.3}X } = 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