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 May 3rd, 2013, 11:16 AM #1 Newbie   Joined: Apr 2013 Posts: 18 Thanks: 0 Equation with variable in exponent Hi How I can solve this: $x^{{2x^2}-9x+4} < 1$ ?? I tried to solve the bhaskara of exponent and use the x value to see how is more less than 1 but, I think it's wrong
May 3rd, 2013, 11:23 AM   #2
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Re: Equation with variable in exponent

Quote:
 Originally Posted by Bencz Hi How I can solve this: $x^{{2x^2}-9x+4} < 1$ ?? I tried to solve the bhaskara of exponent and use the x value to see how is more less than 1 but, I think it's wrong
Sorry, I forgot one thing...

It's to solve the equation in $\mathbb{R}_{+}$

 May 3rd, 2013, 02:25 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,931 Thanks: 1125 Math Focus: Elementary mathematics and beyond Re: Equation with variable in exponent $x^{2x^2\,-\,9x\,+\,4}\,\lt\,1\,\Rightarrow\,x^{(2x\,-\,1)(x\,-\,4)}\,\lt\,1\,\Rightarrow\,x\,\in\,\(0,\,\frac12\ )\,\cup\,\(1,\,4)$
May 4th, 2013, 04:09 PM   #4
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Re: Equation with variable in exponent

Quote:
 Originally Posted by Bencz Hi How I can solve this: $x^{{2x^2}-9x+4} < 1$ ?? I tried to solve the bhaskara of exponent and use the x value to see how is more less than 1 but, I think it's wrong
$x^{{2x^2}-9x+4}<1$

* $x^{a}=< 1=<=> a=<0=$

thus, $x^{{2x^2}-9x+4} <1$
$lt;=> 2x{2} - 9x + 4=<0=<=> (2x-1)(x-4)=<0 ......=$
Good luck!

May 4th, 2013, 04:14 PM   #5
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Re: Equation with variable in exponent

Quote:
Originally Posted by rs_lyly2009
Quote:
 Originally Posted by Bencz Hi How I can solve this: $x^{{2x^2}-9x+4} < 1$ ?? I tried to solve the bhaskara of exponent and use the x value to see how is more less than 1 but, I think it's wrong
$x^{{2x^2}-9x+4}<1$

* $x^{a}=< 1=<=> a=<0=$

thus, $x^{{2x^2}-9x+4} <1$
$lt;=> 2x{2} - 9x + 4=<0=<=> (2x-1)(x-4)=<0 ......=$
Good luck!
I think I'm wrong with latex code

$x^{{2x^2}-9x+4}<1$

* $x^{a}=< 1=<=> a=<0=$

thus, $x^{{2x^2}-9x+4} <1$
$lt;=> 2x{2} - 9x + 4=<0=$

<=> $(2x-1)(x-4) <0 ......$

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