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Sofia8787
@Sofia8787
July 2022
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Lg(1-3x)-1=1/logx√10
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sangers1959
Verified answer
Lg(1-3x)-1=1/logₓ√10
ОДЗ: 1-3x>0 3x<1 x<1/3 x>0 x≠1 ⇒ x(0;1/3)
1. lg(1-3x)-1=lg(1-3x)-lg10=lg((1-3x)/10).
2. 1/logₓ√10=1/logₓ10¹/²=1/((1/2)*logₓ10)=2/logₓ10=2*lgx=lgx². ⇒
lg((1-3x)/10)=lgx²
(1-3x)/10=x²
1-3x=10x²
10x²+3x-1=0 D=49
x=0,2=1/5 ∈ОДЗ x=-0,5 ∉ОДЗ.
Ответ: x=0,2.
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Verified answer
Lg(1-3x)-1=1/logₓ√10ОДЗ: 1-3x>0 3x<1 x<1/3 x>0 x≠1 ⇒ x(0;1/3)
1. lg(1-3x)-1=lg(1-3x)-lg10=lg((1-3x)/10).
2. 1/logₓ√10=1/logₓ10¹/²=1/((1/2)*logₓ10)=2/logₓ10=2*lgx=lgx². ⇒
lg((1-3x)/10)=lgx²
(1-3x)/10=x²
1-3x=10x²
10x²+3x-1=0 D=49
x=0,2=1/5 ∈ОДЗ x=-0,5 ∉ОДЗ.
Ответ: x=0,2.