Question

Решите уравнения log0,5 x + 3 logx 0,5 = 4 5 log3 x - 3 logx 3 = 2 log0,3 x + 9 logx 0,3 = 10

Answer 1

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