算(0.125)^-1/3*16^3/4-3^log底数根号3真数4+log底数3真数32*log底数1/2真数9的值要写清楚过程

题目

算(0.125)^-1/3*16^3/4-3^log底数根号3真数4+log底数3真数32*log底数1/2真数9的值要写清楚过程

答案

(0.125)^(-1/3)*16^(3/4)-3^log√3(4)+log3(32)*log1/2(9)
=(0.5^3)^(-1/3)*(2^4)^(3/4)-[(√3)^2]^log√3(4)+[lg32/lg3]*[lg9/lg(1/2)]
=0.5^[3*(-1/3)]*2^[4*(3/4)]-(√3)^[2*log√3(4)]+[lg2^5/lg3]*[lg3^2/lg2^(-1)]
=(1/2)^(-1)*2^3-(√3)^[log√3(4^2)]+(5lg2/lg3)*(-2lg3/lg2)
=2*8-4^2+5*(-2)*(lg2/lg3)*(lg3/lg2)
=16-16-10
=-10