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June 4th, 2016, 02:07 AM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  exponential inequality
If $\displaystyle 5^x+\left(2\sqrt{3}\right)2^x\geq 13^x\;,$ Then $\displaystyle x$ lies in the interval

June 4th, 2016, 03:10 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
There is no simple "algebraic" way to get an exact solution. By graphing, x must be less than about 0.96.
Last edited by Country Boy; June 4th, 2016 at 03:13 AM. 
June 4th, 2016, 03:25 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,927 Thanks: 2205 
x $\small\leqslant$ 0.94239...


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