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  • 求值:-log2log2√√√2 ,log4 (8)-log1/9 (3)-log√2 (4) ; (log4(3))*(log9(25))*(log5(8))

    求值:-log2log2√√√2 ,log4 (8)-log1/9 (3)-log√2 (4) ; (log4(3))*(log9(25))*(log5(8))
    數(shù)學(xué)人氣:758 ℃時間:2020-02-05 14:49:26
    優(yōu)質(zhì)解答
    -log2log2√√√2
    =-log2 log2 2的1/8次冪
    =-log2 (1/8)
    =log2 8
    =3
    log4 (8)-log1/9 (3)-log√2 (4)
    =log4 4的(3/2)次冪 - 1÷[log3 (1/9)] - log√2 √2的4次冪
    =3/2 - 1÷[log3 (3的-2次冪)] - 4
    =3/2 + 1/2 -4
    =2
    (log4(3))*(log9(25))*(log5(8))
    =(lg3/lg4)*(lg25/lg9)*(lg8/lg5)
    =lg3/(2lg2)*(lg5/lg3)*(3lg2/lg5)
    =3/2
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