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Why is 3^x > e^x > 2^x when x>0, but 3^x < e^x < 2^x when x<0???

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- Thread starter gillgill
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- #1

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Why is 3^x > e^x > 2^x when x>0, but 3^x < e^x < 2^x when x<0???

- #2

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so 3^1=3

2.72^1=2.72

2^1=2

therefore 3^x>e^x>2^x when x>0

however, when you get into the negatives

3^-1=1/3

2.72^-1=1/2.72

2^-1=1/2

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

- #3

EnumaElish

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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.gillgill said:Why is 3^x > e^x > 2^x when x>0, but 3^x < e^x < 2^x when x<0???

- #4

HallsofIvy

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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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