Is it a paradox or I am an idiot.

[zero7860]

please help.

 

[Phrzby Phil]

I worked this for x and y each = 10, in particular, integers.

In step 5, where you divide each side of the inequality by log(1/x), the division was by a negative number [log(1/10) = -1].

So in step 5 you must also reverse the inequality sign.

Cool example.

 

[zero7860]

thank you
but what if 0<x<1 then it would be positive

 

[zero7860]

sorry now I know, in step 8 I have to switch the sign
thank you

 

[Phrzby Phil]

As you see, I just tested with integers. I quietly left it to you for (proper) fractions - which you did. Always good to test general statements with different actual numbers to get a feel for what is really happening.

 

[zero7860]

guess I'll try. thanks btw