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Кариночка78
@Кариночка78
July 2022
1
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Помогите, пожалуйста, вычислить. Подробно.
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oganesbagoyan
Verified answer
784. 1)
( (Log₂ 24 -(1/2)*Log₂ 72 ) / (Log₃18 - (1/3)*Log₃ 72) =
( Log₂ 2³+ Log₂ 3 -(1/2)*(Log₂ 2³ +Log₂ 3² ) ) /
( Log₃3² +Log
₃ 2
-
(1/3)*
(Log₃3²+ Log₃ 2³
) ) =
(3 + Log₂ 3 - 3/2 - Log₂ 3) / (2 +Log₃ 2 - 2/3 - Log₃ 2 ) =(3/2) / (4/3) =9/8 .
========
784. 3)
(Log₂ 4 +Log₂ √10 ) /( Log₂ 20 +3Log
₂ 2 ) =
(2 + (1/2)*(Log₂ 2 +Log₂ 5 ) /( Log₂ 4+Log₂ 5 +3*1 ) =
(1/2)*(5 + Log₂ 5 ) / (5 +Log₂ 5
) = 1/2 .
1 votes
Thanks 5
oganesbagoyan
Log_a M*N = Log_a M + Log_a N и Log_a M^n =n Log_a M , M, N > 0
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Answers & Comments
Verified answer
784. 1) ( (Log₂ 24 -(1/2)*Log₂ 72 ) / (Log₃18 - (1/3)*Log₃ 72) =( Log₂ 2³+ Log₂ 3 -(1/2)*(Log₂ 2³ +Log₂ 3² ) ) /
( Log₃3² +Log₃ 2 - (1/3)* (Log₃3²+ Log₃ 2³) ) =
(3 + Log₂ 3 - 3/2 - Log₂ 3) / (2 +Log₃ 2 - 2/3 - Log₃ 2 ) =(3/2) / (4/3) =9/8 .
========
784. 3) (Log₂ 4 +Log₂ √10 ) /( Log₂ 20 +3Log₂ 2 ) =
(2 + (1/2)*(Log₂ 2 +Log₂ 5 ) /( Log₂ 4+Log₂ 5 +3*1 ) =
(1/2)*(5 + Log₂ 5 ) / (5 +Log₂ 5 ) = 1/2 .