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Resolver desigualdades/ 14^(1+lg(x))/(7*lg^2(100*x)*lg(0,1x))>=4*2^log(10*x)*1/(4*log(100*x)^2*log(x/10))

14^(1+lg(x))/(7*lg^2(100*x)*lg(0,1x))>=4*2^log(10*x)*1/(4*log(100*x)^2*log(x/10)) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
       1 + log(x)                log(10*x)    
     14                       4*2             
--------------------- >= ---------------------
     2           /x \         2           /x \
7*log (100*x)*log|--|    4*log (100*x)*log|--|
                 \10/                     \10/
14log⁡(x)+1log⁡(x10)7log⁡(100x)2≥4⋅2log⁡(10x)4log⁡(100x)2log⁡(x10)\frac{14^{\log{\left(x \right)} + 1}}{\log{\left(\frac{x}{10} \right)} 7 \log{\left(100 x \right)}^{2}} \geq \frac{4 \cdot 2^{\log{\left(10 x \right)}}}{4 \log{\left(100 x \right)}^{2} \log{\left(\frac{x}{10} \right)}} 
14^(log(x) + 1)/((log(x/10)*(7*log(100*x)^2))) >= (4*2^log(10*x))/(((4*log(100*x)^2)*log(x/10)))
Solución de la desigualdad en el gráfico
0123456-5-4-3-2-1-5050
Respuesta rápida 2 [src] 
                                      -1                    
                               -----------------            
                               -log(14) + log(2)            
                     /  log(2)\                             
                     |10      |                             
(0, 1/100) U (1/100, |--------|                 ] U (10, oo)
                     \   2    /
x in (0,1100)∪(1100,(10log⁡(2)2)−1−log⁡(14)+log⁡(2)]∪(10,∞)x\ in\ \left(0, \frac{1}{100}\right) \cup \left(\frac{1}{100}, \left(\frac{10^{\log{\left(2 \right)}}}{2}\right)^{- \frac{1}{- \log{\left(14 \right)} + \log{\left(2 \right)}}}\right] \cup \left(10, \infty\right) 
x in Union(Interval.open(0, 1/100), Interval.Lopen(1/100, (10^log(2)/2)^(-1/(-log(14) + log(2)))), Interval.open(10, oo))
Respuesta rápida [src] 
  /                          /                       1                   \                     \
  |                          |               -----------------           |                     |
  |                          |               -log(2) + log(14)           |                     |
  |                          |     /  log(2)\                            |                     |
  |                          |     |10      |                            |                     |
Or|And(0 < x, x < 1/100), And|x <= |--------|                 , 1/100 < x|, And(10 < x, x < oo)|
  \                          \     \   2    /                            /                     /
(0<x∧x<1100)∨(x≤(10log⁡(2)2)1−log⁡(2)+log⁡(14)∧1100<x)∨(10<x∧x<∞)\left(0 < x \wedge x < \frac{1}{100}\right) \vee \left(x \leq \left(\frac{10^{\log{\left(2 \right)}}}{2}\right)^{\frac{1}{- \log{\left(2 \right)} + \log{\left(14 \right)}}} \wedge \frac{1}{100} < x\right) \vee \left(10 < x \wedge x < \infty\right) 
((0 < x)∧(x < 1/100))∨((10 < x)∧(x < oo))∨((1/100 < x)∧(x <= (10^log(2)/2)^(1/(-log(2) + log(14)))))
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