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Resolver desigualdades/ log((x),(20x+3(x)^2+(x)^3))=>3

log((x),(20x+3(x)^2+(x)^3))=>3 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
   /             2    3\     
log\x, 20*x + 3*x  + x / >= 3
log⁡(x)≥3\log{\left(x \right)} \geq 3 
log(x, x^3 + 3*x^2 + 20*x) >= 3
Solución de la desigualdad en el gráfico
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.0-5000050000
Respuesta rápida [src] 
   /                                                                                             ________________                          \
   |                                                                                            /        _______                           |
   |       / 8      7       6        5         4         3         2       \                   /  19   \/ 88197                17          |
And|CRootOf\x  + 9*x  + 87*x  + 387*x  + 1740*x  + 3600*x  + 8000*x  - 1, 1/ <= x, x < -1 + 3 /   -- + ---------  - -----------------------|
   |                                                                                        \/    2        18              ________________|
   |                                                                                                                      /        _______ |
   |                                                                                                                     /  19   \/ 88197  |
   |                                                                                                                3*3 /   -- + --------- |
   \                                                                                                                  \/    2        18    /
CRootOf⁡(x8+9x7+87x6+387x5+1740x4+3600x3+8000x2−1,1)≤x∧x<−173192+88197183−1+192+88197183\operatorname{CRootOf} {\left(x^{8} + 9 x^{7} + 87 x^{6} + 387 x^{5} + 1740 x^{4} + 3600 x^{3} + 8000 x^{2} - 1, 1\right)} \leq x \wedge x < - \frac{17}{3 \sqrt[3]{\frac{19}{2} + \frac{\sqrt{88197}}{18}}} - 1 + \sqrt[3]{\frac{19}{2} + \frac{\sqrt{88197}}{18}} 
(x < -1 + (19/2 + sqrt(88197)/18)^(1/3) - 17/(3*(19/2 + sqrt(88197)/18)^(1/3)))∧(CRootOf(x^8 + 9*x^7 + 87*x^6 + 387*x^5 + 1740*x^4 + 3600*x^3 + 8000*x^2 - 1, 1) <= x)
Respuesta rápida 2 [src] 
                                                                                                                   _________________ 
                                                                                         3 ____          3 ____ 3 /         _______  
        / 8      7       6        5         4         3         2       \             17*\/ 18           \/ 12 *\/  171 + \/ 88197   
[CRootOf\x  + 9*x  + 87*x  + 387*x  + 1740*x  + 3600*x  + 8000*x  - 1, 1/, -1 - ---------------------- + ---------------------------)
                                                                                     _________________                6              
                                                                                  3 /         _______                                
                                                                                3*\/  171 + \/ 88197
x in [CRootOf⁡(x8+9x7+87x6+387x5+1740x4+3600x3+8000x2−1,1),−171833171+881973−1+123171+8819736)x\ in\ \left[\operatorname{CRootOf} {\left(x^{8} + 9 x^{7} + 87 x^{6} + 387 x^{5} + 1740 x^{4} + 3600 x^{3} + 8000 x^{2} - 1, 1\right)}, - \frac{17 \sqrt[3]{18}}{3 \sqrt[3]{171 + \sqrt{88197}}} - 1 + \frac{\sqrt[3]{12} \sqrt[3]{171 + \sqrt{88197}}}{6}\right) 
x in Interval.Ropen(CRootOf(x^8 + 9*x^7 + 87*x^6 + 387*x^5 + 1740*x^4 + 3600*x^3 + 8000*x^2 - 1, 1), -17*18^(1/3)/(3*(171 + sqrt(88197))^(1/3)) - 1 + 12^(1/3)*(171 + sqrt(88197))^(1/3)/6)
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