Mister Exam
log(3-x,((x+4)/(x-3)^2))>2 inequation
The solution
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[src]
/ x + 4 \ log|3 - x, --------| > 2 | 2| \ (x - 3) /
$$\log{\left(3 - x \right)} > 2$$
log(3 - x, (x + 4)/(x - 3)^2) > 2
Detail solution
Given the inequality:
$$\log{\left(3 - x \right)} > 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(3 - x \right)} = 2$$
Solve:
$$x_{1} = 4.84395478913155 - 1.54531734705023 i$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$\log{\left(3 - 0 \right)} > 2$$
so the inequality has no solutions
$$\log{\left(3 - x \right)} > 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(3 - x \right)} = 2$$
Solve:
$$x_{1} = 4.84395478913155 - 1.54531734705023 i$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0
$$\log{\left(3 - 0 \right)} > 2$$
log(3) -------- > 2 log(4/9)
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
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/ ____ \ | / 5 4 3 2 \ 7 \/ 29 | And|x < CRootOf\x - 15*x + 90*x - 269*x + 413*x - 227, 0/, - - ------ < x| \ 2 2 /
$$x < \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 90 x^{3} - 269 x^{2} + 413 x - 227, 0\right)} \wedge \frac{7}{2} - \frac{\sqrt{29}}{2} < x$$
(7/2 - sqrt(29)/2 < x)∧(x < CRootOf(x^5 - 15*x^4 + 90*x^3 - 269*x^2 + 413*x - 227, 0))
Rapid solution 2
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____ 7 \/ 29 / 5 4 3 2 \ (- - ------, CRootOf\x - 15*x + 90*x - 269*x + 413*x - 227, 0/) 2 2
$$x\ in\ \left(\frac{7}{2} - \frac{\sqrt{29}}{2}, \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 90 x^{3} - 269 x^{2} + 413 x - 227, 0\right)}\right)$$
x in Interval.open(7/2 - sqrt(29)/2, CRootOf(x^5 - 15*x^4 + 90*x^3 - 269*x^2 + 413*x - 227, 0))