1.
а) Log_1/21 ∛21 = -1/3.
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б) (1-Log_6 54)(1-Log_9 54)=(1-(Log_6 6 +Log_6 9) )(1 -(Log_9 9 +Log_9 6))=
(1 -1-Log_6 9) )(1 -1 -Log_9 6))=(-Log_6 9)*((-Log_9 6 ) =1.
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в) (7^Log_5 3) ^(Log_7 5) = (7^Log_7 5)^(Log_5 3) = 5 ^(Log_5 3) =3.
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2.
* * * Log _a b = Log _a^k b^k * * *
а) 4^(0,5Log_4 9 - 0,25Log_2 25) = (2² ) ^ (0,5Log_4 9 - 0,25Log_2 25)=
2 ^ 2*(0,5Log_4 9 - 0,25Log_2 25)=2^ ( Log_4 9 -0,5Log_2 25) =
=2^ ( Log_2 3 -0,5*2Log_2 5) = 2^ ( Log_2 3 -Log_2 5) = 2^ ( Log_2 3/5) =3/5.
---или иначе
4^(0,5Log_4 9 - 0,25Log_2 25) = 4^(0,5Log_4 3² - 0,25Log_2 5²)=
4^(0,5*2Log_4 3 - 0,25*2Log_2 5) = 4^(Log_4 3 - 0,5Log_2 5) =
4^(Log_4 3 - 0,5Log_4 25) =4^(Log_4 3 - 0,5*2Log_4 5) =
4^(Log_4 3 - Log_4 5) = 4^(Log_4 3/5 ) =3/5 .
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б) Log_3 7 /Log_3 5 * Log_7 5/Log_2 5 -Log_5 10 =
(Log_3 7*Log_7 5) /(Log_3 5 * Log_2 5) -(Log_5 2+Log_5 5)=
(Log_3 5)/(Log_3 5 * Log_2 5)- Log_5 2-1 =1/ (Log_2 5) - Log_5 2-1=
Log_5 2 -Log_5 2 -1 = -1.
---или иначе
Log_3 7 /Log_3 5 * Log_7 5/Log_2 5 -Log_5 10 =
Log_5 7 * ( Log_7 5)*(Log_5 2) - (Log_5 2+Log_5 5) =
1*(Log_5 2) - Log_5 2-Log_5 5 = -1.