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  • Inequation:
  • 7-9x>3
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  • -3*x^2+4<0
  • 0,5^x>0,5
  • 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 minus 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 minus 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

  • 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
Solving inequalities/ 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

A inequation with variable

The solution

You have entered [src] 
   / 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:
$$x_{1} = 9$$
$$x_{2} = - \frac{\left(-1\right)^{\frac{2}{3}} \left(144 \sqrt[3]{2} + \sqrt[3]{-1} \left(1 - \sqrt{3} i\right) \left(12 + \sqrt[3]{-1} \cdot 2^{\frac{2}{3}} \left(1 - \sqrt{3} i\right) \sqrt[3]{163 - \sqrt{3241}}\right) \sqrt[3]{163 - \sqrt{3241}}\right)}{4 \left(1 - \sqrt{3} i\right) \sqrt[3]{163 - \sqrt{3241}}}$$
$$x_{3} = - \frac{\left(-1\right)^{\frac{2}{3}} \left(144 \sqrt[3]{2} + \sqrt[3]{-1} \left(1 + \sqrt{3} i\right) \left(12 + \sqrt[3]{-1} \cdot 2^{\frac{2}{3}} \left(1 + \sqrt{3} i\right) \sqrt[3]{163 - \sqrt{3241}}\right) \sqrt[3]{163 - \sqrt{3241}}\right)}{4 \left(1 + \sqrt{3} i\right) \sqrt[3]{163 - \sqrt{3241}}}$$
$$x_{4} = 3 - \frac{2^{\frac{2}{3}} \sqrt[3]{-163 + \sqrt{3241}}}{2} + \frac{18 \left(-1\right)^{\frac{2}{3}} \sqrt[3]{2}}{\sqrt[3]{163 - \sqrt{3241}}}$$
Exclude the complex solutions:
$$x_{1} = 9$$
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
$$\left(9 - x\right) \log{\left(\left(- 27 x + \left(x^{3} - 9 x^{2}\right)\right) - 27 \right)} \geq 0$$
$$\left(9 - \frac{89}{10}\right) \log{\left(\left(- \frac{27 \cdot 89}{10} + \left(- 9 \left(\frac{89}{10}\right)^{2} + \left(\frac{89}{10}\right)^{3}\right)\right) - 27 \right)} \geq 0$$
   /275221\            
log|------|            
   \ 1000 /   pi*I >= 0
----------- + ----     
     10        10

Then
$$x \leq 9$$
no execute
the solution of our inequality is:
$$x \geq 9$$
         _____  
        /
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       x1
Solving inequality on a graph
Rapid solution [src] 
   /              ________________                                                  \
   |             /         ______                                                   |
   |            /  163   \/ 3241               18                 3 ___      2/3    |
And|x <= 3 + 3 /   --- + --------  + ---------------------, 3 + 3*\/ 2  + 3*2    < x|
   |         \/     2       2             ________________                          |
   |                                     /         ______                           |
   |                                    /  163   \/ 3241                            |
   |                                 3 /   --- + --------                           |
   \                                 \/     2       2                               /
$$x \leq 3 + \frac{18}{\sqrt[3]{\frac{\sqrt{3241}}{2} + \frac{163}{2}}} + \sqrt[3]{\frac{\sqrt{3241}}{2} + \frac{163}{2}} \wedge 3 + 3 \sqrt[3]{2} + 3 \cdot 2^{\frac{2}{3}} < x$$ 
(3 + 3*2^(1/3) + 3*2^(2/3) < x)∧(x <= 3 + (163/2 + sqrt(3241)/2)^(1/3) + 18/(163/2 + sqrt(3241)/2)^(1/3))
Rapid solution 2 [src] 
                                   ________________                       
                            2/3 3 /         ______             3 ___      
       3 ___      2/3      2   *\/  163 + \/ 3241           18*\/ 2       
(3 + 3*\/ 2  + 3*2   , 3 + ------------------------ + -------------------]
                                      2                  ________________ 
                                                      3 /         ______  
                                                      \/  163 + \/ 3241
$$x\ in\ \left(3 + 3 \sqrt[3]{2} + 3 \cdot 2^{\frac{2}{3}}, 3 + \frac{18 \sqrt[3]{2}}{\sqrt[3]{\sqrt{3241} + 163}} + \frac{2^{\frac{2}{3}} \sqrt[3]{\sqrt{3241} + 163}}{2}\right]$$ 
x in Interval.Lopen(3 + 3*2^(1/3) + 3*2^(2/3), 3 + 18*2^(1/3)/(sqrt(3241) + 163)^(1/3) + 2^(2/3)*(sqrt(3241) + 163)^(1/3)/2)
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