Exponential And Logarithmic Inequality

[MayaMaya121]

Hi,
Can someone help me solve this exponential and logarithmic inequality? I just can't find the simplest way to solve this...
[MATH]x^{\log \:_3\left(4x^2-8x+6\right)}<x[/MATH]I did the following steps:
(Assuming that x and [MATH]x^{\log \:_3\left(4x^2-8x+6\right)}[/MATH] are positive numbers)
[MATH]x^{\log \:_3\left(4x^2-8x+6\right)}<x[/MATH] [MATH]\\log _3\left(\right)[/MATH] On both sides.
[MATH]\log _3\left(x\right)\cdot \log _3\left(4x^2-8x+6\right)<\log _3\left(x\right)[/MATH] [MATH]\div \log _3\left(x\right)[/MATH] On both sides.
Then I split the inequality to two parts: [MATH]\log _3\left(x\right)[/MATH] is negative or positive.

Is there a more simple way to solve this?
There are not statements about x apart from x being a rational number. The instructions are just to solve the inequality.

 

[Dr.Peterson]

Where does it say that x is rational? And why would that matter? What's important is that x should be positive.

But what you did is what I would do, if I could assume x is positive.

In any case, don't look for the simplest way. Look for a solution, then use that to consider other possibilities.

 

[MayaMaya121]

Ok, Thank you.