задача с логарифмами во вложении. Created by NormickMcCormick. algebra-ru

задача с логарифмами во вложении...

mmb1

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log(a^k) b^n = n/k log(a) b

log(c) (ab) = log(c) a + log(c) b

log(2) (log(3) 2.25 + log(3) log(2) 16) = log(2) (log(3) 2.25 + log(3) log(2) 2^4) = log(2) (log(3) 2.25 + log(3) 4) = log(2) log(3) 2.25*4 = log(2) log(3) 3^2 = log(2) 2 = 1

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Universalka

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$log_{2}(log_{3}2,25+log_{3}log_{2}16)=log_{2}(log_{3}2,25+log_{3}4)=log_{2}(log_{3}(1,25*4))=log_{2}log_{3}9=log_{2}2=1$

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Answers & Comments

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