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ycilko
@ycilko
March 2022
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Решите логарифмическое уравнение
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mikael2
Verified answer
X>9 1/2 log5 (2x-1)+1/2log5(x-9)=log5 10
log5 (2x-1)(x-9)=log5 100
(2x-1)(x-9)=100
2x²-x-18x+9-100=0
2x²-19x-91=0 D=19²+8*91=361+728=1089 √1089=33
x1=1/4[19+33]=13 x2=1/4[19-33]<9
ответ 13
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Answers & Comments
Verified answer
X>9 1/2 log5 (2x-1)+1/2log5(x-9)=log5 10log5 (2x-1)(x-9)=log5 100
(2x-1)(x-9)=100
2x²-x-18x+9-100=0
2x²-19x-91=0 D=19²+8*91=361+728=1089 √1089=33
x1=1/4[19+33]=13 x2=1/4[19-33]<9
ответ 13