Why is 3^x > e^x > 2^x when x>0, but 3^x < e^x < 2^x when x<0???
e is approx. 2.72
therefore 3^x>e^x>2^x when x>0
however, when you get into the negatives
this is because a negative power indicates an inverse( 1/x ), so the smaller the number with a negative power, the smaller the denomenator will be
Another way of looking at it. Since 3 > e and therefore Log(3) > 1, x Log(3) > x implies x > 0 and x Log(3) < x implies x < 0.
All this is saying is that if 0<a< b< c then 0< 1/c< 1/b< 1/a
If a< b and a and b are positive, then 1< b/a because we have divided by a positive number.
Then 1/b< 1/a because we have divided by a positive number.
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