Question

lg2x*lgx=lg5 x=?

Answer 1

(lgx)^2+lg2*lgx=lg5

利用换低公式得到以a为低的样子

（logaX/loga10)^2+(loga2/loga10)*(logaX/loga10)=loga5/loga10

((logaX)^2+loga2*logaX)=loga5*loga10

((logaX)^2+loga2*logaX)=loga5*(loga5+loga2)

((logaX)^2+loga2*logaX)=(loga5)^2+loga5*loga2

(logaX+loga5)*(logaX-log5)+loga2*(logaX-loga5)=0

loga(X/5)*loga(5X)+loga2(loga(X/5)=0

loga(X/5)(loga5X+loga2)=0

loga(X/5)loga10X=0

所以

x/5=1 or 10x=1

得到

x=5 or x=1/10