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Tanya6164
@Tanya6164
September 2021
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кто силен в логарифмах?
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sedinalana
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9x²+5 и 8x^4+14 больше 0 при любом х,значит х∈(-∞;∞)
log(2)2+log(2)(9x²+5)=log(2)(8x^4+14)
log(18x²+10)=log(2)(8x^4+14)
18x²+10=8x^4+14
x²=a
8a²-18a+4=0
4a²-9a+2=0
D=81-32=49
a1=(9-7)/8=1/4⇒x²=1/4
x=-1/2∈[-1;8/9]
x=1/2∈[-1;8/9]
a2=(9+7)/8=2⇒x²=2
x=-√2∉[-1;8/9]
x=√2∉[-1;8/9]
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Answers & Comments
Verified answer
9x²+5 и 8x^4+14 больше 0 при любом х,значит х∈(-∞;∞)log(2)2+log(2)(9x²+5)=log(2)(8x^4+14)
log(18x²+10)=log(2)(8x^4+14)
18x²+10=8x^4+14
x²=a
8a²-18a+4=0
4a²-9a+2=0
D=81-32=49
a1=(9-7)/8=1/4⇒x²=1/4
x=-1/2∈[-1;8/9]
x=1/2∈[-1;8/9]
a2=(9+7)/8=2⇒x²=2
x=-√2∉[-1;8/9]
x=√2∉[-1;8/9]