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Evelina0889
@Evelina0889
August 2021
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Sos 10-11 класс логарифмы
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1) log₂ log₅ (⁸√ 5)=log₂ log₅ ( 5^(1/8))=log₂(1/8)=log₂(2^(-3))=-3
2)log²₃ log (1/125)=log²₃ log ((1/5)^3)=(log₃3)²=1²=1
1/5 1/5
4) log log₃₄₃ 49= log log 7²= (log [(1/3)log₇7²])=(log 2/3)=1
2/3 2/3 7³ 2/3 2/3
5) log₄ log₃ (√ 81)= log₄ log₃ ( 3²)=log₄(2)=log₄(4^(1/2))=1/2
7) log²₉ log₂8= log²₉ log₂2³=(log₉ 3)²=[log₉ (9^(1/2))]²=1/4
8) log₂ log 49 =log₂ (2log 7²)=log₂(2·2)=log₂2²=2
√7 7
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Answers & Comments
Verified answer
1) log₂ log₅ (⁸√ 5)=log₂ log₅ ( 5^(1/8))=log₂(1/8)=log₂(2^(-3))=-32)log²₃ log (1/125)=log²₃ log ((1/5)^3)=(log₃3)²=1²=1
1/5 1/5
4) log log₃₄₃ 49= log log 7²= (log [(1/3)log₇7²])=(log 2/3)=1
2/3 2/3 7³ 2/3 2/3
5) log₄ log₃ (√ 81)= log₄ log₃ ( 3²)=log₄(2)=log₄(4^(1/2))=1/2
7) log²₉ log₂8= log²₉ log₂2³=(log₉ 3)²=[log₉ (9^(1/2))]²=1/4
8) log₂ log 49 =log₂ (2log 7²)=log₂(2·2)=log₂2²=2
√7 7