2log(b)x=log(a)x+log(c)x求证,c^2=(ac)^[log(a)b]

2log(b)x=log(a)x+log(c)x求证,c^2=(ac)^[log(a)b]
2log(b)x=log(a)x+log(c)x
求证,c^2=(ac)^[log(a)b]

2log(b)x=log(a)x+log(c)x求证,c^2=(ac)^[log(a)b]
2log(b)x=log(a)x+log(c)x
2lgx/lgb=lgx/lga+lgx/lgc
把lgx约分
2/lgb=1/lga+1/lgc=(lga+lgc)/(lgalgc)=lg(ac)/(lgalgc)
(lgb)/2=lgalgc/lg(ac)
lgb/lga=2lgc/lg(ac)=lgc^2/lg(ac)
所以loga(b)=log(ac)c^2
(ac)^loga(b)=(ac)^log(ac)c^2
所以(ac)^loga(b)=c^2