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charizardik64
@charizardik64
July 2022
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Решите уравнение
[tex]log_{3}(3 x^{2} ) * log_{3} x =1[/tex]
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mmb1
Verified answer
Log3 (3x^2) * log3 x = 1
одз x>0
log ab = log !a ! + log !b!
(log3 3 + log3 x^2)*log3 x =1
(1 + 2log3 x)*log3 x = 1
2log3^2 x + log3x - 1=0
log3 x =t
2t^2+t-1=0
D=1+8=9
t12=(-1+-3)/4= - 1 1/2
log3 x=-1
x=1/3
log3 x=1/2
x=√3
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Answers & Comments
Verified answer
Log3 (3x^2) * log3 x = 1одз x>0
log ab = log !a ! + log !b!
(log3 3 + log3 x^2)*log3 x =1
(1 + 2log3 x)*log3 x = 1
2log3^2 x + log3x - 1=0
log3 x =t
2t^2+t-1=0
D=1+8=9
t12=(-1+-3)/4= - 1 1/2
log3 x=-1
x=1/3
log3 x=1/2
x=√3