一道整式题求解.log0.5x(x^2) - 14log16x(x^3) + 40log4x(根号下x）=0求xloga

log2(x^2)/log2(0.5x)-14log2(x^3)/
log2(16x)+40log2(x^0.5)/log2(4x)=0
将原式都转换成以2为底的对数
2log2(x)/[log2(0.5)+log2(x)]-42log2(x)/[log2(16)+log2(x)]+20log2(x)/[log2(4)+log2(x)]=0
log2(x)/[-1+log2(x)]-21log2(x)/[4+log2(x)]+10log2(x)/[2+log2(x)]=0
[log2(x)]{1/[-1+log2(x)]-21/[4+log2(x)]+10/[2+log2(x)]}=0
通分
[log2(x)]=0
化简
[log2(x)]=0
[log2(x)][1+2log2(x)][-2+log2(x)]/[-1+log2(x)][4+log2(x)][2+log2(x)]=0
所以：log2(x)=0或1+2log2(x)=0或-2+log2(x)=0
解得：x=1;x=1/根号2；x=4

loga^n(b^m)=m/n*loga(b)
log0.5x(x^2)=-2log2x(x)
14log16x(x^3)=14*3/4*log2x(x)=21/2log2x(x)
40log4x(√x)=40/2*1/2**log2x(x)=10log2x(x)
原式=-2log2x(x)-21/2log2x(x)+10log2x(x)=0
-3/2log2x(x)=0
log2x(x)=0
x=1或x=2/√e或 x=2e^2

log0.5x(x^2) - 14log16x(x^3) + 40log4x(√x)=0 (x>0)
lnx^2/ln(0.5x)-14lnx^3/ln(16x)+40ln√x/ln(4x)=0
2lnx/(lnx-ln2)-42lnx/(lnx+4ln2)+20lnx/(lnx+2ln2)=0
令t=lnx,a=ln2,则：
2t/(t-a)-42/(t+4a)...

log0.5x(x^2) - 14 log16x(x^3) + 40 log4x(√x）=0
求x
log0.5x(x^2)-14log16x(x^3)+40log4x(x^0.5）=0
log0.5x(x^2)+40log4x(x^0.5)=14log16x(x^3)
log0.5x(x^2)+log4x(x^0.5)^40=log16x(x^3)^14

log0.5x(x^2)
=2log0.5x(x)
=2lg(x)/lg(0.5x)
=2lg(x)/[lg(0.5)+lg(x)]
=2lg(x)/[-lg(2)+lg(x)]
14log16x(x^3)
=42log16x(x)
=42lg(x)/lg(16x)
=42lg(x)/[lg(16)+lg(x)]
=...