Решите уравнение Лог2(5+4х)=лог2(1-4х)+1. Created by anastasiya315. matematika-ru

Решите уравнение Лог2(5+4х)=лог2(1-4х)+1...

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ОДЗ: 5 + 4x > 0 и 1-4x > 0
x > -1,25 и x < 0,25
log2(5+4x) = log2(1-4x) + log2(2)
log2(5+4x) = log2((1-4x)* 2)
5 + 4x = 2 - 8x
12x = -3
x = -0,25

Ответ: -0,25

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ЕкарныйБабай

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Log2(5+4х)=log2(1-4х)+1
ОДЗ
5+4x>0 4x>-5 x>-5/4
1-4x>0 4x<1 x<1/4
log2(5+4x)=log2(1-4x)+log2 2
log2(5+4x)=log2 2(1-4x)
5+4x=2-8x
12x=-3
x=-3/12=-1/4 по ОДЗ проходит

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