# Logarithm Inequality

Log x ((x+3)/(x-1) > Log x x ??

I've managed to find 4 conditions for this inequality:
1. -1 > x > 3
2. x > -3
3. x > 0
4. x ≠ 1

but I'm not sure how to write the solution. Is it " 0 < x & 1 < 0 < 3 " ?

Thanks.

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Office_Shredder
Staff Emeritus
Gold Member
1. -1 > x > 3
I think you mistyped what this is supposed to be.

If you have multiple conditions, just write them out the way you would state them in English. For example, if I asked for the solutions to |x|>1 I would write "x>1 or x<-1". If someone asked for the solutions to |x2-4| > 1, I would write " x>sqrt(5) or -sqrt(3)<x<sqrt(3) or x<-sqrt(5)".

Notice you will never have an and condition. If you wrote something like " 1<x<5 and 2<x<7" you should just replace that with "2<x<5". If you have two conditions that are incompatible, just say there are no solutions rather than writing something like "1<x<3 and 5<x<6"

I think you mistyped what this is supposed to be.

If you have multiple conditions, just write them out the way you would state them in English. For example, if I asked for the solutions to |x|>1 I would write "x>1 or x<-1". If someone asked for the solutions to |x2-4| > 1, I would write " x>sqrt(5) or -sqrt(3)<x<sqrt(3) or x<-sqrt(5)".

Notice you will never have an and condition. If you wrote something like " 1<x<5 and 2<x<7" you should just replace that with "2<x<5". If you have two conditions that are incompatible, just say there are no solutions rather than writing something like "1<x<3 and 5<x<6"

Hi. Thank you for the reply.

Could you help me to find x that would satisfy the inequality?

Office_Shredder
Staff Emeritus