解方程log2(x^2-3)=log2(6x-10)-1
问题描述：
解方程log2(x^2-3)=log2(6x-10)-1
答
log[2(x^2-3)]=log[2(6x-10)]-1
lg[2(x^2-3)]=lg[2(6x-10)]-lg10
lg[2(x^2-3)]=lg{[2(6x-10)]/10}
lg[2(x^2-3)]=lg[(6x-10)/5]
2(x^2-3)=(6x-10)/5
10(x^2-3)=6x-10
10x^2-30=6x-10
10x^2-6x-20=0
5x^2-3x-10=0
x=(3±√209)/10
x1=(3+√209)/10
x2=(3-√209)/10
答
log2(x^2-3)=log2(6x-10)-1即log2(x^2-3)=log2(6x-10)/2x²-3=(6x-10)/2①x²-3>0②6x-10>0③由①得2x²-6=6x-102x²-6x+4=0x²-3x+2=0(x-1)(x-2)=0x=1或x=2又因为必须满足②③,所以代入检验发...