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Solve inequality (1/3)^x>=1/27?
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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]` .
Posted by sciencesolve on July 11, 2013 at 4:38 PM (Answer #1)
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