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oksanko24
@oksanko24
December 2021
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Логарифмы. Очень нужна ваша помощь, прям ну ооочень очень.
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sangers1959
Verified answer
1) 5*9^log₉2=5*2=10.
2) 25^log₅9=5^(2*log₅9)=5^log₅9²=9²=81.
3) log₀,₂25=log₁/₅5²=log₁/₅(1/5)⁻²=-2.
4)log₄64=log₄4³=3*log₄4=3.
5) log₈512=log₈8³=3.
6)log₂₀300-log₂₀0,75=log₂₀(300/0,75)=log₂₀400=log₂₀20²=2.
7) log₄32+log₀,₁10=log₂²(2⁵)+log₁/₁₀10=(1/2)log₂2⁵+log₁/₁₀(1/10)⁻¹=
=5/2-1=1,5.
8) log₀,₃₅20-log₀,₃₅7=log₀,₃₅(20/7)=log₇/₂₀(7/20)⁻¹=-1.
9) log₃8/log₃2=log₃2³/log₃2=3*log₃2/log₃2=3.
10) log₂14/log₄14=log₂14/log₂²14=log₂14/((1/2)*log₂14)=1/(1/2)=2.
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Answers & Comments
Verified answer
1) 5*9^log₉2=5*2=10.2) 25^log₅9=5^(2*log₅9)=5^log₅9²=9²=81.
3) log₀,₂25=log₁/₅5²=log₁/₅(1/5)⁻²=-2.
4)log₄64=log₄4³=3*log₄4=3.
5) log₈512=log₈8³=3.
6)log₂₀300-log₂₀0,75=log₂₀(300/0,75)=log₂₀400=log₂₀20²=2.
7) log₄32+log₀,₁10=log₂²(2⁵)+log₁/₁₀10=(1/2)log₂2⁵+log₁/₁₀(1/10)⁻¹=
=5/2-1=1,5.
8) log₀,₃₅20-log₀,₃₅7=log₀,₃₅(20/7)=log₇/₂₀(7/20)⁻¹=-1.
9) log₃8/log₃2=log₃2³/log₃2=3*log₃2/log₃2=3.
10) log₂14/log₄14=log₂14/log₂²14=log₂14/((1/2)*log₂14)=1/(1/2)=2.