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Feirte
@Feirte
October 2021
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Помогите решить логарифм
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sangers1959
Verified answer
1) Упростим первое слагаемое:
x^(1+1/(2*log₄x)=x^(1+(1/2)*logx(4))=x^(1+logx(√4))=
=x^(logx(x)+logx(2))=x^logx(2x)=2x.
2) Упростим второе слагаемое:
8^(1/*3*logx²(2))=2^(3/3*logx²(2))=2^1/logx²(2)=2^log₂x²=x². ⇒
3) (2x+x²+1)¹/²=√(x²+2x+1)=√(x+1)²
=x+1
.
2 votes
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Answers & Comments
Verified answer
1) Упростим первое слагаемое:x^(1+1/(2*log₄x)=x^(1+(1/2)*logx(4))=x^(1+logx(√4))=
=x^(logx(x)+logx(2))=x^logx(2x)=2x.
2) Упростим второе слагаемое:
8^(1/*3*logx²(2))=2^(3/3*logx²(2))=2^1/logx²(2)=2^log₂x²=x². ⇒
3) (2x+x²+1)¹/²=√(x²+2x+1)=√(x+1)²=x+1.