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47ranono
@47ranono
October 2021
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Логарифмические уравнения 80б. Срочно, помогите
1]log 4-x по основанию 2 равно 2
Найти х
2)log x-3 по осн 1/4 равно -1
3)log (x^2-3х-10) по осн 2 равно 3
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1)log2 (4-x)=2, 4-x bolše čem 0, x menše čem 4, x∈(-∞,4)
4-x=2², 4-x=4, -x=0,x=0
===
2)log(1/4) (x-3)= -1, x∈(3,∞)
x-3=(1/4)ˇ-1, x-3=4ˇ1,x-3=4,x=7
===
3)log2 (x²-3x-10)=3 , x∈(-∞,-2)∪(5,∞)
x²-3x-10=2³, x²-3x-10=8, x²-3x-18=0,(x-6)(x+3)=0
x1=6, 6∈(5,∞)
x2=-3, -3∈(-∞,-2)
6 i -3 rešeniem.
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Answers & Comments
4-x=2², 4-x=4, -x=0,x=0
===
2)log(1/4) (x-3)= -1, x∈(3,∞)
x-3=(1/4)ˇ-1, x-3=4ˇ1,x-3=4,x=7
===
3)log2 (x²-3x-10)=3 , x∈(-∞,-2)∪(5,∞)
x²-3x-10=2³, x²-3x-10=8, x²-3x-18=0,(x-6)(x+3)=0
x1=6, 6∈(5,∞)
x2=-3, -3∈(-∞,-2)
6 i -3 rešeniem.