2^(log9/log4)=?
請給我長盡的過程
ｔｈｘ
有一條log的數不識做
2008-02-29 7:48 pm
回答 (3)
2008-02-29 7:56 pm
✔ 最佳答案
log 9 / log 4 = 2 log 3 / 2 log 2
= log 3 / log 2
Let 2^( log 9 / log 4 ) = y,
log y = ( log 9 / log 4 )( log 2 )
log y = ( log 3 / log 2 )( log 2 )
log y = log 3
y = 3
Therefore 2^( log 9 / log 4 ) = 3
參考: My Maths Knowledge
2008-02-29 8:39 pm
設 x = 2^(log9/log4) 就好易做啦
log(x) = log(2^(log9/log4)) = (log9)/(log4) x log(2) = 2log(3) * log(2) / (2log(2)) = log(3)
Therefore x = 3.
log(x) = log(2^(log9/log4)) = (log9)/(log4) x log(2) = 2log(3) * log(2) / (2log(2)) = log(3)
Therefore x = 3.
2008-02-29 8:17 pm
2^(log9/log4)
= 2^(log(3^2) / log(2^2))
= 2^( 2log(3) / 2log(2) )
= 2^( log(3)/log(2) )
= 2^( log2(3) ) ... log2(3) means log of 3 in base of 2
= 3
Usally, we use log(x) indicates log of x in base of 10.
= 2^(log(3^2) / log(2^2))
= 2^( 2log(3) / 2log(2) )
= 2^( log(3)/log(2) )
= 2^( log2(3) ) ... log2(3) means log of 3 in base of 2
= 3
Usally, we use log(x) indicates log of x in base of 10.
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