Выразить log300120 через a и b если a=log23 n=log35. Created by tanyatimchenko. algebra-ru

Выразить log300120 через a и b если a=log23 n=log35...

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Выразить log300120 через a и b если a=log23 n=log35

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MizoriesKun 120=5*3*8=5*3*2³
300=25*3*4=5²*3*2²
㏒₂ 120 ㏒₂ 5*3*2³ ㏒₂ 5+㏒₂ 3+3㏒₂ 2
㏒₃₀₀120= ---------------- = ------------------ = ------------------------------- =
㏒₂ 300 ㏒₂ 5²*3*2² 2㏒₂ 5+㏒₂ 3+ 2㏒₂ 2

㏒₃5
а+㏒₂ 5+3 а+3 + ----------
㏒₃2 а+3+ ㏒₃5* ㏒₂3 а+3+n*a
= ------------------- = --------------------- = -------------------------- = -------------------
а+2㏒₂ 5+2 2 ㏒₃ 5 а+2+2 ㏒₃5* ㏒₂3 a+2+2n*a
а+2+ ------------
㏒₃2

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