若logx表示log10x(10为底数),且log(5x^2)=a,则log(4/x^4)=?求过程!!!!!!!!!!!!

Question

若logx表示log10x(10为底数),且log(5x^2)=a,则log(4/x^4)=?
求过程!!!!!!!!!!!!

Answer 1

解由log(5x^2)=a,
得log5+log(x^2)=a
即log(x^2)=a-log5
故log(4/x^4)
=log(4)-log(x^4)
=2log(2)-2log(x^2)
=2log(2)-2(a-log5)
=2log(2)+2log5-2a
=2(log(2)+log5)-2a
=2log(2*5)-2a
=2log(10)-2a
=2-2a