lg2x*lgx=lg5怎么算

(lgx+lg2)lgx-(1-lg2)=0
lg²x+lg2lgx-(1-lg2)=0
[lgx-(1-lg2)](lgx+1)=0
(lgx-lg5)(lgx+1)=0
lgx=lg5,lgx=-1
所以x=5,x=1/10

lg2x*lgx=log(2x+x)=log3x=lg5
3x=5
x=5/3

lg2x*lgx=lg5
(lg2+lgx)*lgx=lg5
(lgx)^2+lg2lgx=lg5
(lgx)^2+lg2lgx-lg5=0
(lgx)^2+lg2lgx-(1-lg2)=0
(lgx)^2-1+lg2lgx+lg2=0
(lgx-1)(lgx+1)+lg2(lgx+1)=0
(lgx-1+lg2)(lgx+1)=0
(lgx-lg5)(lgx+1)=0
lgx=lg5或lgx+1=0
所以x=5 或x=1/10

lg2x*lgx=(lg2+lgx)lgx=(lgx)^2+lg2*lgx=lg5
=> (lgx)^2+lg2*lgx-lg5=0
解方程，得
lgx=[-lg2+√(lg2)^2+4lg5]/2 或lgx=[-lg2-√(lg2)^2+4lg5]/2
因为lg2=lg(10/5)=1-lg5
=> lgx=lg5 或lgx=-1
解得 x=5 或x=1/10

lg2x*lgx=lg(2x+x)=lg3x=lg5
3x=5
x=5/3

希望能帮你忙，不懂请追问，懂了请采纳，谢谢

lg2x*lgx=lg5
(lg2+lgx)lgx=lg5
(lgx)^2+lg2*x-lg5=0
(lgx+1)(lgx-lg5)=0
lgx=-1或lgx=lg5
x=5或x=1/10