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Resolver desigualdades/ 5^sqrt64^(3x-1)>sqrt(1/6)^(1-3x/x-1)

5^sqrt64^(3x-1)>sqrt(1/6)^(1-3x/x-1) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
                              3*x    
 /      3*x - 1\          1 - --- - 1
 |  ____       |               x     
 \\/ 64        /   /  1  \           
5                > |-----|           
                   |  ___|           
                   \\/ 6 /
$$5^{\left(\sqrt{64}\right)^{3 x - 1}} > \left(\sqrt{\frac{1}{6}}\right)^{\left(1 - \frac{3 x}{x}\right) - 1}$$ 
5^((sqrt(64))^(3*x - 1)) > (sqrt(1/6))^(1 - 3*x/x - 1)
Respuesta rápida 2 [src] 
          /   /    ___\\     
          |log\6*\/ 6 /|     
     2*log|------------|     
 1        \   log(5)   /     
(- + -------------------, oo)
 3        3*log(64)
$$x\ in\ \left(\frac{2 \log{\left(\frac{\log{\left(6 \sqrt{6} \right)}}{\log{\left(5 \right)}} \right)}}{3 \log{\left(64 \right)}} + \frac{1}{3}, \infty\right)$$ 
x in Interval.open(2*log(log(6*sqrt(6))/log(5))/(3*log(64)) + 1/3, oo)
Respuesta rápida [src] 
   /                 /   /    ___\\    \
   |                 |log\6*\/ 6 /|    |
   |            2*log|------------|    |
   |        1        \   log(5)   /    |
And|x < oo, - + ------------------- < x|
   \        3        3*log(64)         /
$$x < \infty \wedge \frac{2 \log{\left(\frac{\log{\left(6 \sqrt{6} \right)}}{\log{\left(5 \right)}} \right)}}{3 \log{\left(64 \right)}} + \frac{1}{3} < x$$ 
(x < oo)∧(1/3 + 2*log(log(6*sqrt(6))/log(5))/(3*log(64)) < x)
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