作业帮log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 05:06:59
![log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}](/uploads/image/z/13887071-71-1.jpg?t=log%281%2F2%29%28x%5E2-5x-6%29%3Elog2%7B1%2F%5B2%28x%2B6%29%5D%7D)
log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}
log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}
log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}
首先
x^2-5x-6>0
得 x>6或x0
得 x>-6
所以-6log(1/2)(2(x+6))
因为以1/2为底的对数是减函数
所以x^2-5x-6
log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}
原式等价为：1/(x^2-5x-6)<1/[2(x+6)]
原式等价为：1/(x^2-5x-6)-1/[2(x+6)]<0
通分，并进行分母因式分解，分子合并同类项、因式分解，等价为：
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log(1/2)(x^2-5x-6)>log2{1/[2(x+6)]}