log以3为底x的对数的号外平方+log以9为底3x的对数=2

显示全部楼层 · 2012-11-6 13:56:52

[log3(x)]2+log9(3x)=2 log9(3x)=(1/2)log3(3x)=(1/2)[log3(3)+log3(x)]=1/2+(1/2)log3(x) 所以，原方程化为：[log3(x)]2+(1/2)log3(x)+1/2=2即：[log3(x)]2+(1/2)log3(x)-3/2=0
2[log3(x)]2+log3(x)-3=0令log3(x)=t，则2t2+t-3=0
(t-1)(2t+3)=0
t1=1，t2=-3/2log3(...

千问 · 2012-11-6 13:56:52

(log3 x)^2+log9 (3x)=2(lgx/lg3)^2+(lg3x)/lg9=2(lgx)^2/(lg3)^2+(lg3+lgx)/2lg3=22(lgx)^2+(lg3+lgx)lg3=4(lg3)^22(lgx)^2+lg3lgx-3(lg3)^2=0(2lgx+3lg3)(lgx-lg3)=02lgx+3lg3=...

千问 · 2012-11-6 13:56:52

[log3(x)]^2+log9(3x)=2令log3(x)=tlog9(3x)=(1/2)[1+log3(x)]=1/2+t/2t^2+t/2+1/2=22t^2+t-3=0(2t+3)(t-1)=0t=-3/2或t=1x=3^(-3/2)或x=3...