(log4^3+log5^3)(log3^2+log4^2)-log0.5^4倍根号32

来源：百度知道 编辑：UC知道 时间：2024/05/18 01:38:35

(log4^3+log5^3)(log3^2+log4^2)-log0.5^4倍根号32
=(lg3/lg4+lg3/lg5)(lg2/lg3+lg2/lg4)-log0.5^4*4根号2
=(lg3/2lg2+lg3/lg5)(lg2/lg3+lg2/2lg2)-log0.5^2^(9/2)
=(lg3/2lg2+lg3/lg5)(lg2/lg3+1/2)-(9/2)lg2/lg0.5
=lg3/2lg2*lg2/lg3+lg3/2lg2*1/2+lg3/lg5*lg2/lg3+lg3/lg5*1/2-(9/2)*lg2/(-lg2)
=1/2+lg3/4lg2+lg2/lg5+(1/2)lg3/lg5+9/2
=5+(1/4)log2(3)+log5(2√3)

用换底公式来做就行