Question

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

Answer 1

-log2log2√√√2
=-log2 log2 2的1/8次幂
=-log2 (1/8)
=log2 8
=3

log4 (8)-log1/9 (3)-log√2 (4)
=log4 4的(3/2)次幂 - 1÷[log3 (1/9)] - log√2 √2的4次幂
=3/2 - 1÷[log3 (3的-2次幂)] - 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