求[lg^2(5)-lg^2(2)/lg25-lg4]*log(1/2)1/4+8^[log(4)(3/5)^2]的值
问题描述：
求[lg^2(5)-lg^2(2)/lg25-lg4]*log(1/2)1/4+8^[log(4)(3/5)^2]的值
答
[lg^2(5)-lg^2(2)/lg25-lg4]*log(1/2)1/4+8^[log(4)(3/5)^2]
=[(lg(5)+lg(2))(lg(5)-lg(2))/2(lg5-lg2)]*log(1/2)(1/2)^2+2^3[log(4)(3/5)^2]
=[(lg(5)+lg(2))/2]*2+2^2[log(4)(3/5)^3]
=(1/2)*2+4^[log(4)(3/5)^3]
=1+(3/5)^3
=1+27/125
=152/125