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emmma
#1 Posted : Monday, February 13, 2012 3:21:17 PM
Rank: Newbie

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Joined: 2/13/2012
Posts: 1

2^3x< 1/4^x

 

Help, anyone? I have been wondering this for awhile now... Thanks for the help :)
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talouv
#2 Posted : Thursday, March 22, 2012 1:12:04 AM
Rank: Newbie

Groups: Registered Users

Joined: 3/22/2012
Posts: 2

Hi Emma

Your question is when the unequality holds?

I guess that you might have forgotten some parentheses, so that the equation would be

2^{3x}<\left(\frac{1}{4}\right)^x

Well, the solutions is that it holds for some x.

You should realize that (1/4)^x is decreasing, while 2^(3x) is increasing. So what we have to do is to solve the equation

2^{3x}=\left(\frac{1}{4}\right)^x

You'll se that this holds excatly when x=0 (both are then euqal to 1).

With this in mind, you can conclude that

2^{3x}<\left(\frac{1}{4}\right)^x \Leftrightarrow x<0

You could also try to draw the two functions with some kind of graph calculator or with the free Windows program Graph.
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