作业帮log3(x+2)-log3(x方-x-6)+1>0答案和过程!
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log3(x+2)-log3(x方-x-6)+1>0答案和过程!
log3(x+2)-log3(x方-x-6)+1>0答案和过程!
log3(x+2)-log3(x方-x-6)+1>0答案和过程!
logaB-logaC=loga(B/C)
log3(x+2)-log3(x^2-x-6)=log3[(x+2)/(x^2-x-6)]
然后把1移到右边就是-1 -1=log3(1/3)
所以就是log3[(x+2)/(x^2-x-6)] > log3(1/3)
即：
(x+2)/(x^2-x-6) > 1/3
把三分之一移到不等号左边,化简：
[(X-6)(X+2)]/[(X-3)(X+2)] < 0
(X-6)(X-3) < 0
3< X
(1)定义域
x+2>0
x^2-x-6>0
=> x>3
log3(x+2)-log3(x^2-x-6)+1>0
log3(x+2)-log3[(x-3)(x+2)]+1>0
log3(x+2)-log3(x-3)-log3(x+2)+1>0
1-log3(x-3)>0
log3(x-3)<1
0
哈哈，楼上的回答太搞笑啦
X-3<3
x<0?????
x+2>0 x>-2
x^2-x-6>0 (x-3)(x+2)>0 x>3或x<-2
所以满足x>3
log3[3(x+2)/(x^2-x-6)]>0
log3[3/(x-3)]>0
3/(x-3)>3
1/(x-3)>1
0
x+2>0 x>-2
x^2-x-6>0 (x-3)(x+2)>0 x>3
∴x>3
log3(x+2)-log3(x^2-x-6)+1>0
log3(x+2)-log3[(x-3)(x+2)]+1>0
log3(x+2)-log3(x-3)-log3(x+2)+1>0
1-log3(x-3)>0
log3(x-3)<1
x-3<3
x<6
∴3
log3(X+2)-log3(X2次方-X-6)+1>0
log3【(X+2)/(X2次方-X-6)*3】>0
则(X+2)/(X²-X-6)*3 ＞1，X+2＞0，X²-X-6＞0.
可得3＜x＜6.
首先保证真数为正，有x+2>0且x²-x-6>0，联立解得
x>3
由log3(x+2)-log3(x²-x-6)+1>0变形得
log3(x+2)-log3[(x-3)(x+2)]>-1
log3{(x+2)/[(x-3)(x+2)]}> log3(1/3)
log3[1/(x-3)]> log3(1/3)
1/(x-3)>1/...
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首先保证真数为正，有x+2>0且x²-x-6>0，联立解得
x>3
由log3(x+2)-log3(x²-x-6)+1>0变形得
log3(x+2)-log3[(x-3)(x+2)]>-1
log3{(x+2)/[(x-3)(x+2)]}> log3(1/3)
log3[1/(x-3)]> log3(1/3)
1/(x-3)>1/3
前面已得出x>3，所以x-3>0，所以上式两边同乘以x-3，不等式不变号，得
1>( x-3)/3，解之得x<6，
与前面的x>3取交集得
3
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