log2(x+1)+log2(x+8)=3的解集是?

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log2(x+1)+log2(x+8)=3的解集是?
log2(x+1)+log2(x+8)=3的解集是?

log2(x+1)+log2(x+8)=3的解集是?
∵log2(x+1)+log2(x+8)=3
∴log2[(x+1)(x+8)]=3
∴(x+1)(x+8)=2^3=8
∴x^2+9x=0
x(x+9)=0
x1=0,x2=-9
x+1＞0
∴x＞-1
x+8＞0
∴x＞-8
综合:x＞-1
∴解集是x=0

{0}
同时满足x+1>0
x+8>0
(x+1)(x+8)=8
x=0或x=-9（舍）
所以x=0

{x|x=0}

由条件：log2(x+1)+log2(x+8)=3
得x+1>0
x+8>0
(x+1)(x+8)=2^3=8
解得：x=0(x=-9不符合x>-8,舍去）
解集是{x|x=0}

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