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Ragnfreed
@Ragnfreed
November 2021
2
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Упростите выражение. Если можно, с объяснением.
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kirichekov
Verified answer
Решение во вложении------------
2 votes
Thanks 1
Ragnfreed
Спасибо огромнейшее!
Марика07
Воспользуемся формулами: log₂(14)=log₂7+log₂2=log₂7+1 и log₇2=1/log₂7
получаем
((log₂7+1)²+(log₂7+1)*log₂7-2(log₂7)²)/((log₂7+1)*1/log₂7+2)=((log₂7)²+2log₂7+1+(log₂7)²+log₂7-2(log₂7)²)/((log₂7+1+2log₂7):log₂7)=(3log₂7+1)*log₂7:(3log₂7+1)=
log₂7
1 votes
Thanks 1
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Решение во вложении------------получаем
((log₂7+1)²+(log₂7+1)*log₂7-2(log₂7)²)/((log₂7+1)*1/log₂7+2)=((log₂7)²+2log₂7+1+(log₂7)²+log₂7-2(log₂7)²)/((log₂7+1+2log₂7):log₂7)=(3log₂7+1)*log₂7:(3log₂7+1)=log₂7