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Basto2
@Basto2
July 2022
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Решите уравнение: ㏒₂(3ˣ+6)+log₂(3ˣ-1)=3 А) ㏒₂3 B) ㏒₃2 C) ㏒₃4 D) 1 E) 4
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mmb1
Verified answer
㏒₂(3ˣ+6)+log₂(3ˣ-1)=3
одз 3ˣ>1 x>0
㏒₂(3ˣ+6)+log₂(3ˣ-1)=㏒₂8
(3ˣ+6)(3ˣ-1)=8
3ˣ=t t>0
(t+6)(t-1)=8
t²+6t-t-6-8=0
t²+5t-14=0
D=25+56=81
t12=(-5+-9)/2= - 7 2
-7 нет
3ˣ=2
x=㏒₃ 2
ответ В
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Answers & Comments
Verified answer
㏒₂(3ˣ+6)+log₂(3ˣ-1)=3одз 3ˣ>1 x>0
㏒₂(3ˣ+6)+log₂(3ˣ-1)=㏒₂8
(3ˣ+6)(3ˣ-1)=8
3ˣ=t t>0
(t+6)(t-1)=8
t²+6t-t-6-8=0
t²+5t-14=0
D=25+56=81
t12=(-5+-9)/2= - 7 2
-7 нет
3ˣ=2
x=㏒₃ 2
ответ В