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  • Desigualdades:
  • (x-2)/(x-4)>0 (x-2)/(x-4)>0
  • (x-7)(x+8)>0
  • -x^2-10x-24>0 -x^2-10x-24>0
  • (x+8)(x-5)>0 (x+8)(x-5)>0

  • Expresiones idénticas

  • ocho /log2 uno 6x>= tres /log28x+1/log22x
  • 8 dividir por logaritmo de 216x más o igual a 3 dividir por logaritmo de 28x más 1 dividir por logaritmo de 22x
  • ocho dividir por logaritmo de 2 uno 6x más o igual a tres dividir por logaritmo de 28x más 1 dividir por logaritmo de 22x
  • 8 dividir por log216x>=3 dividir por log28x+1 dividir por log22x

  • Expresiones semejantes

  • 8/log216x>=3/log28x-1/log22x
Resolver desigualdades/ 8/log216x>=3/log28x+1/log22x

8/log216x>=3/log28x+1/log22x desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
    8             3           1    
---------- >= --------- + ---------
log(216*x)    log(28*x)   log(22*x)
8log⁡(216x)≥3log⁡(28x)+1log⁡(22x)\frac{8}{\log{\left(216 x \right)}} \geq \frac{3}{\log{\left(28 x \right)}} + \frac{1}{\log{\left(22 x \right)}} 
8/log(216*x) >= 3/log(28*x) + 1/log(22*x)
Solución de la desigualdad en el gráfico
0123456789-5-4-3-2-110-100100
Respuesta rápida [src] 
  /                             /                          _______________________________________________________________________________________________________                \                                  _______________________________________________________________________________________________________     \
  |                             |                         /       2             2              2                                                                                  |                                 /       2             2              2                                                                       |
  |                             |                      -\/  25*log (22) + 49*log (28) + 144*log (6) - 120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22)                 |                               \/  25*log (22) + 49*log (28) + 144*log (6) - 120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22)      |
  |                             |                      ------------------------------------------------------------------------------------------------------------               |                               ----------------------------------------------------------------------------------------------------------     |
  |                             |    ___   3/8 8 ____                                                       8                                                                     |             ___   3/8 8 ____                                                      8                                                          |
  |                             |3*\/ 3 *11   *\/ 14 *e                                                                                                                           |         3*\/ 3 *11   *\/ 14 *e                                                                                                               |
Or|And(1/216 < x, x < 1/28), And|---------------------------------------------------------------------------------------------------------------------------------- <= x, x < 1/22|, x = 0, -------------------------------------------------------------------------------------------------------------------------------- <= x|
  \                             \                                                               154                                                                               /                                                                       154                                                                    /
(1216<x∧x<128)∨(3⋅11381483154e−120log⁡(6)log⁡(28)−58log⁡(22)log⁡(28)+24log⁡(6)log⁡(22)+25log⁡(22)2+144log⁡(6)2+49log⁡(28)28≤x∧x<122)∨x=0∨3⋅11381483e−120log⁡(6)log⁡(28)−58log⁡(22)log⁡(28)+24log⁡(6)log⁡(22)+25log⁡(22)2+144log⁡(6)2+49log⁡(28)28154≤x\left(\frac{1}{216} < x \wedge x < \frac{1}{28}\right) \vee \left(\frac{3 \cdot 11^{\frac{3}{8}} \sqrt[8]{14} \sqrt{3}}{154 e^{\frac{\sqrt{- 120 \log{\left(6 \right)} \log{\left(28 \right)} - 58 \log{\left(22 \right)} \log{\left(28 \right)} + 24 \log{\left(6 \right)} \log{\left(22 \right)} + 25 \log{\left(22 \right)}^{2} + 144 \log{\left(6 \right)}^{2} + 49 \log{\left(28 \right)}^{2}}}{8}}} \leq x \wedge x < \frac{1}{22}\right) \vee x = 0 \vee \frac{3 \cdot 11^{\frac{3}{8}} \sqrt[8]{14} \sqrt{3} e^{\frac{\sqrt{- 120 \log{\left(6 \right)} \log{\left(28 \right)} - 58 \log{\left(22 \right)} \log{\left(28 \right)} + 24 \log{\left(6 \right)} \log{\left(22 \right)} + 25 \log{\left(22 \right)}^{2} + 144 \log{\left(6 \right)}^{2} + 49 \log{\left(28 \right)}^{2}}}{8}}}{154} \leq x 
(x = 0))∨((1/216 < x)∧(x < 1/28))∨(3*sqrt(3)*11^(3/8)*14^(1/8)*exp(sqrt(25*log(22)^2 + 49*log(28)^2 + 144*log(6)^2 - 120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22))/8)/154 <= x)∨((x < 1/22)∧(3*sqrt(3)*11^(3/8)*14^(1/8)*exp(-sqrt(25*log(22)^2 + 49*log(28)^2 + 144*log(6)^2 - 120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22))/8)/154 <= x)
Respuesta rápida 2 [src] 
                                                 _______________________________________________________________________________________________________                                     _______________________________________________________________________________________________________     
                                                /       2             2              2                                                                                                      /       2             2              2                                                                       
                                             -\/  25*log (22) + 49*log (28) + 144*log (6) - 120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22)                                   \/  25*log (22) + 49*log (28) + 144*log (6) - 120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22)      
                                             ------------------------------------------------------------------------------------------------------------                                 ----------------------------------------------------------------------------------------------------------     
                           ___   3/8 8 ____                                                       8                                                                     ___   3/8 8 ____                                                      8                                                          
                       3*\/ 3 *11   *\/ 14 *e                                                                                                                       3*\/ 3 *11   *\/ 14 *e                                                                                                               
{0} U (1/216, 1/28) U [----------------------------------------------------------------------------------------------------------------------------------, 1/22) U [--------------------------------------------------------------------------------------------------------------------------------, oo)
                                                                                      154                                                                                                                                         154
x in {0}∪(1216,128)∪[3⋅11381483154e−120log⁡(6)log⁡(28)−58log⁡(22)log⁡(28)+24log⁡(6)log⁡(22)+25log⁡(22)2+144log⁡(6)2+49log⁡(28)28,122)∪[3⋅11381483e−120log⁡(6)log⁡(28)−58log⁡(22)log⁡(28)+24log⁡(6)log⁡(22)+25log⁡(22)2+144log⁡(6)2+49log⁡(28)28154,∞)x\ in\ \left\{0\right\} \cup \left(\frac{1}{216}, \frac{1}{28}\right) \cup \left[\frac{3 \cdot 11^{\frac{3}{8}} \sqrt[8]{14} \sqrt{3}}{154 e^{\frac{\sqrt{- 120 \log{\left(6 \right)} \log{\left(28 \right)} - 58 \log{\left(22 \right)} \log{\left(28 \right)} + 24 \log{\left(6 \right)} \log{\left(22 \right)} + 25 \log{\left(22 \right)}^{2} + 144 \log{\left(6 \right)}^{2} + 49 \log{\left(28 \right)}^{2}}}{8}}}, \frac{1}{22}\right) \cup \left[\frac{3 \cdot 11^{\frac{3}{8}} \sqrt[8]{14} \sqrt{3} e^{\frac{\sqrt{- 120 \log{\left(6 \right)} \log{\left(28 \right)} - 58 \log{\left(22 \right)} \log{\left(28 \right)} + 24 \log{\left(6 \right)} \log{\left(22 \right)} + 25 \log{\left(22 \right)}^{2} + 144 \log{\left(6 \right)}^{2} + 49 \log{\left(28 \right)}^{2}}}{8}}}{154}, \infty\right) 
x in Union(FiniteSet(0), Interval.open(1/216, 1/28), Interval.Ropen(3*11^(3/8)*14^(1/8)*sqrt(3)*exp(-sqrt(-120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22) + 25*log(22)^2 + 144*log(6)^2 + 49*log(28)^2)/8)/154, 1/22), Interval(3*11^(3/8)*14^(1/8)*sqrt(3)*exp(sqrt(-120*log(6)*log(28) - 58*log(22)*log(28) + 24*log(6)*log(22) + 25*log(22)^2 + 144*log(6)^2 + 49*log(28)^2)/8)/154, oo))
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