Пожалуйста помогите) Решите логарифмические уравнения:
1) [tex]3 lg^{2}( x-1) -10lg( x-1) +3=0[/tex]
2) [tex] \frac{1}{5-lgx} + \frac{2}{1+lgx} =1[/tex]
3) [tex] lg^{2}(100x) + lg^{10x}=14+ lg \frac{1}{x} [/tex]
4) [tex] lg^{2} x- 2lgx= lg^{2}100-1 [/tex]
1) [tex]3 lg^{2}( x-1) -10lg( x-1) +3=0[/tex]
2) [tex] \frac{1}{5-lgx} + \frac{2}{1+lgx} =1[/tex]
3) [tex] lg^{2}(100x) + lg^{10x}=14+ lg \frac{1}{x} [/tex]
4) [tex] lg^{2} x- 2lgx= lg^{2}100-1 [/tex]
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Verified answer
3*lg²(x-1)-10*lg(x-1)+3=0lg(x-1)=t ⇒
3t²-10t+3=0 D=64
t₁=3 lg(x-1)=3 x-1=10³ x₁=1001
t₂=1/3 lg(x-1)=1/3 x-1=∛10 x₂=∛10+1
1/(5-lgx)+2/(1+lgx)=1
1+lgx+10-2lgx=-lg²x+4lgx+5
lg²x-5lgx+6=0
lgx=t ⇒
t²-5t+6=0 D=1
t₁=2 lgx=2 x₁=10²=100
t₂=3 lgx=3 x₂=10³=1000
lg²x-2lgx=lg²100-1
lg²x-2lgx=2²-1
lg²x-2lgx-3=0
lgx=t
t²-2t-3=0 D-16
t₁=3 lgx=3 x=1000
t₂=-1 lgx=-1 x=1/10.