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

Question

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

Answer 1

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