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December 12th, 2015, 05:56 AM  #1 
Member Joined: Aug 2014 From: Lithuania Posts: 60 Thanks: 3  A problem with logarithms
I need to solve this: $\displaystyle \log_2 (3xx^22)>=3^{x+2}$ I know that $\displaystyle (3xx^22)>0$, so $\displaystyle x\in(1;2)$. If $\displaystyle f(x)=\log_2 (3xx^22)$ and $\displaystyle g(x)=3^{x+2}$, so $\displaystyle g(x)\in(27;81)$. Since $\displaystyle (3xx^22)$ is a parabola which peaks at 1.5, so $\displaystyle f(x)=[2;0)$. From this I can conclude that there are no solutions. Is this correct? Last edited by kaspis245; December 12th, 2015 at 06:29 AM. 
December 12th, 2015, 07:01 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
At $x = 1.5$, $3x  x^2  2 = 0.25$, so there are no solutions. Are you sure the problem you posted is what you are meant to be solving? 

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