log2(x-1)+log2(x+1)=3的解是?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/27 13:50:17
log2(x-1)+log2(x+1)=3的解是?
x)O7Ҩ5Ԇ 5mjy|m /$T)ѧ{Mtݬ';;Οd.0BXYgÓK+ uL/.H̳_kBML@rl z&(V("TgkhkcZBXO=l []';zNxhƳ_t>~O'6GEm"l'v}ӁЀ\Fu6Ա @WB|2"lQ

log2(x-1)+log2(x+1)=3的解是?
log2(x-1)+log2(x+1)=3的解是?

log2(x-1)+log2(x+1)=3的解是?
log2(x-1)+log2(x+1)=3
log2(x-1)(x+1)=3
函数定义域为
(x-1)(x+1)>0
所以x>1或x

log2x-2+log2x+2=3
4x-2+2=3
4x=3
x=0.75(3/4)

log2(x-1)+log2(x+1)=3
log2(x-1)(x+1)=3
(x-1)(x+1)=2^3
x^2-1=8
x^2=9
x=3(另一根x=-3不合题意要舍去)

X=3

条件log2(x-1)+log2(x+1)=3
得x-1>0
x+1>0
(x-1)(x+1)=2^3=8
得x=3(x=-3不符合x>1,所以舍去)