解方程 logx(2)*log2x(4)=log8x(2)

题目

解方程 logx(2)*log2x(4)=log8x(2)

答案

左=logx(2)*[2logx(2)]^2
=4log3x(2);
右=log8x(2)
则4log3x(2)=log8x(2);
log5x(2)=4;
logx(2)=2^(2/5);
log2(x)=2^(-2/5);
x=2^[2^(-2/5)];