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- Square Inequality Step-by-Step
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How to use it?
- Inequation:
- y^2-4*x+8>0
-
(|x+3|)+4*x>=6
- (sqrt(3)-(sqrt(13)))x>5/(sqrt(3)+sqrt(13))
- logx+1,(x-2)<=1
- Canonical form:
- =0
-
Identical expressions
- log(x^ three - nine *x^ two + twenty-seven *x- twenty-seven)*(nine -x)>= zero
- logarithm of (x cubed minus 9 multiply by x squared plus 27 multiply by x minus 27) multiply by (9 minus x) greater than or equal to 0
- logarithm of (x to the power of three minus nine multiply by x to the power of two plus twenty minus seven multiply by x minus twenty minus seven) multiply by (nine minus x) greater than or equal to zero
- log(x3-9*x2+27*x-27)*(9-x)>=0
- logx3-9*x2+27*x-27*9-x>=0
- log(x³-9*x²+27*x-27)*(9-x)>=0
- log(x to the power of 3-9*x to the power of 2+27*x-27)*(9-x)>=0
- log(x^3-9x^2+27x-27)(9-x)>=0
- log(x3-9x2+27x-27)(9-x)>=0
- logx3-9x2+27x-279-x>=0
- logx^3-9x^2+27x-279-x>=0
- log(x^3-9*x^2+27*x-27)*(9-x)>=O
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Similar expressions
- log(x^3-9*x^2-27*x-27)*(9-x)>=0
- log(x^3+9*x^2+27*x-27)*(9-x)>=0
- log(x^3-9*x^2+27*x-27)*(9+x)>=0
- log(x^3-9*x^2+27*x+27)*(9-x)>=0
log(x^3-9*x^2+27*x-27)*(9-x)>=0 inequation
The solution
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/ 3 2 \ log\x - 9*x + 27*x - 27/*(9 - x) >= 0
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} \geq 0$$
(9 - x)*log(27*x + x^3 - 9*x^2 - 27) >= 0
Detail solution
Given the inequality:
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} = 0$$
Solve:
$$x_{1} = 9$$
$$x_{1} = 9$$
This roots
$$x_{1} = 9$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 9$$
=
$$\frac{89}{10}$$
substitute to the expression
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} \geq 0$$
$$\left(9 - \frac{89}{10}\right) \log{\left(-27 + \left(\left(- 9 \left(\frac{89}{10}\right)^{2} + \left(\frac{89}{10}\right)^{3}\right) + \frac{27 \cdot 89}{10}\right) \right)} \geq 0$$
the solution of our inequality is:
$$x \leq 9$$
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} = 0$$
Solve:
$$x_{1} = 9$$
$$x_{1} = 9$$
This roots
$$x_{1} = 9$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 9$$
=
$$\frac{89}{10}$$
substitute to the expression
$$\left(9 - x\right) \log{\left(\left(27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} \geq 0$$
$$\left(9 - \frac{89}{10}\right) \log{\left(-27 + \left(\left(- 9 \left(\frac{89}{10}\right)^{2} + \left(\frac{89}{10}\right)^{3}\right) + \frac{27 \cdot 89}{10}\right) \right)} \geq 0$$
/205379\
log|------|
\ 1000 / >= 0
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10 the solution of our inequality is:
$$x \leq 9$$
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x1
Solving inequality on a graph