log4^25-2log4^10+log2^9×log3^根号5×log5^2
问题描述：
log4^25-2log4^10+log2^9×log3^根号5×log5^2
答
原式= lg25/lg4-2lg10/lg4+lg9/lg2×lg√5/lg3×lg2/lg5= (2lg5)/(2lg2)-2/(2lg2)+(2lg3)/lg2×(½lg5)/lg3×lg2/lg5= lg5/lg2-1/lg2+1= (lg5-1+lg2)/lg2= (lg5+lg2-1)/lg2= (lg10-1)/lg2= (1-1)/lg2= 0