2.解下列方程;2
21ogx-31og2-5=0
解:
令1ogx=y 则1og2=1/y
2y-3/y-5=0
2y^-5y-3=0
y1=-1/2 x1=(√2)/2
y2=3 x2=8
(8)
1ogx^2-141ogx^3+401og√x=0
401og√x=40log[4x]x^(1/2)=20log[4x]x
=20lgx/lg4x=20lgx/[lg4+lgx]
141ogx^3=42log[16x]x=42lgx/[2lg4+lgx]
1ogx^2=2log[0。 5x]x=2lgx/[lg0。5+lgx]
令lgx=y
2y/[lg0。 5+y]-42y/...全部
21ogx-31og2-5=0
解:
令1ogx=y 则1og2=1/y
2y-3/y-5=0
2y^-5y-3=0
y1=-1/2 x1=(√2)/2
y2=3 x2=8
(8)
1ogx^2-141ogx^3+401og√x=0
401og√x=40log[4x]x^(1/2)=20log[4x]x
=20lgx/lg4x=20lgx/[lg4+lgx]
141ogx^3=42log[16x]x=42lgx/[2lg4+lgx]
1ogx^2=2log[0。
5x]x=2lgx/[lg0。5+lgx]
令lgx=y
2y/[lg0。
5+y]-42y/[2lg4+y]+20y/[lg4+y]=0
2y^-11y×lg2-6lg2=0
y1=-1/2 x1=√10/10
y2=6 x2=10^6
。收起