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Solve inequality (1/3)^x>=1/27?

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nurli | Honors

Posted July 11, 2013 at 4:18 PM via web

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Solve inequality (1/3)^x>=1/27?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 11, 2013 at 4:38 PM (Answer #1)

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You should notice that the base of exponential function is less than 1, but positive, hence, the exponential function decreases over `(0,oo)` .

You should notice that the bigger x values are, the smaller y values become, hence, the red curve descends and it almost touches x axis, as x goes from `-oo` toward `+oo` .

You need to solve the given inequality based on this property of exponential function whose base is less than 1, such that:

`(1/3)^x>=1/27 => (1/3)^x>=(1/3)^3 => x <= 3=> x in (-oo,3]`

Hence, evaluating the interval solution to the given inequality, using the property of exponential function whose base is less than 1, yields ` x in (-oo,3]` .

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user4825270 | Student | eNoter

Posted July 29, 2013 at 8:27 PM (Answer #2)

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1/3^x=1/27
3^-x=3^-3
-x=-3
x=3

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