解方程log2(x^2-3)=log2(6x-10)-1

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解方程log2(x^2-3)=log2(6x-10)-1

解方程log2(x^2-3)=log2(6x-10)-1
解方程log2(x^2-3)=log2(6x-10)-1

解方程log2(x^2-3)=log2(6x-10)-1
log2(x^2-3)=log2(6x-10)-1

log2(x^2-3)=log2(6x-10)/2
x²-3=(6x-10)/2①
x²-3>0②
6x-10>0③
由①得
2x²-6=6x-10
2x²-6x+4=0
x²-3x+2=0
(x-1)(x-2)=0
x=1或x=2
又因为必须满足②③,所以
代入检验发现,x=1不对
所以
x=2

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