Упростите
[tex]\frac{2}{1+log_{15}6+log_{15}2}+\frac{2}{1+log_{6}15+log_{6}2}+\frac{2}{1+log_{2}15+log_{2}6}[/tex]
[tex]\frac{2}{1+log_{15}6+log_{15}2}+\frac{2}{1+log_{6}15+log_{6}2}+\frac{2}{1+log_{2}15+log_{2}6}[/tex]
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Answers & Comments
Упрощаем первое слагаемое:
2/(log₁₅15+log₁₅6+log₁₅)=2/log₁₅(15*6*2)=2/log₁₅180=2*log₁₈₀15.
Аналогично упрощаем второе и третье слагаемые:
2/(log₆6+log₆15+log₆2)=2/log₆180=2*log₁₈₀6.
2/(log₂2+log₂15+log₂6)=2/log₂180=2*log₁₈₀2. ⇒
2*log₁₈₀15+2*log₁₈₀6+2*log₁₈₀2=2*(log₁₈₀15+log₁₈₀6+log₁₈₀2)=
=2*log₁₈₀(15*6*2)=2*log₁₈₀180=2*1=2.