End of school level equation

[Zaiheinles]

I don’t understand how to solve it and in what sequence?

[math]\frac{ \sqrt{4+3x-x^{2}}+x-4 }{ \log_{x}({2x-4})^{2} } \geqslant 0[/math]

 

[Cubist]

My initial thought is to consider two cases. One when the denominator is +ve, and one when it's -ve. What must the numerator be in each case?

Please show some work so that we know where you need help...

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[JeffM]

In addition to the questions asked by cubist, what can we deduce about x from [MATH]log_x[/MATH]?

How about what can be deduced from [MATH]\sqrt{4 + 3x - x^2}[/MATH]?

 

[lex]

Draw a number line and mark the regions where the top line is positive or negative (by first finding where it =0). Also restrict this to the values of x for which the top line exists.

Draw a number line and mark the regions where the bottom line is positive or negative (by first finding where it =0). Also restrict this to the values of x for which the bottom line exists.
(Note [MATH]\log_x (2x-4)^2=0[/MATH] means [MATH](2x-4)^2=1[/MATH])

Use these to find the regions where they both have the same sign (and exist and the fraction itself exists).