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log(x+3)⁴=8 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   4           
log (x + 3) = 8
log⁡(x+3)4=8\log{\left(x + 3 \right)}^{4} = 8
Simplificar
Gráfica
05-15-10-5101505000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
             3/4
           -2   
x1 = -3 + e
x1=−3+e−234x_{1} = -3 + e^{- 2^{\frac{3}{4}}} 
           / 3/4\
           \2   /
x2 = -3 + e
x2=−3+e234x_{2} = -3 + e^{2^{\frac{3}{4}}} 
               / 3/4\      / 3/4\
x3 = -3 - I*sin\2   / + cos\2   /
x3=−3+cos⁡(234)−isin⁡(234)x_{3} = -3 + \cos{\left(2^{\frac{3}{4}} \right)} - i \sin{\left(2^{\frac{3}{4}} \right)} 
               / 3/4\      / 3/4\
x4 = -3 + I*sin\2   / + cos\2   /
x4=−3+cos⁡(234)+isin⁡(234)x_{4} = -3 + \cos{\left(2^{\frac{3}{4}} \right)} + i \sin{\left(2^{\frac{3}{4}} \right)} 
x4 = -3 + cos(2^(3/4)) + i*sin(2^(3/4))
Suma y producto de raíces [src] 
suma
        3/4         / 3/4\                                                              
      -2            \2   /             / 3/4\      / 3/4\             / 3/4\      / 3/4\
-3 + e      + -3 + e       + -3 - I*sin\2   / + cos\2   / + -3 + I*sin\2   / + cos\2   /
(((−3+e−234)+(−3+e234))+(−3+cos⁡(234)−isin⁡(234)))+(−3+cos⁡(234)+isin⁡(234))\left(\left(\left(-3 + e^{- 2^{\frac{3}{4}}}\right) + \left(-3 + e^{2^{\frac{3}{4}}}\right)\right) + \left(-3 + \cos{\left(2^{\frac{3}{4}} \right)} - i \sin{\left(2^{\frac{3}{4}} \right)}\right)\right) + \left(-3 + \cos{\left(2^{\frac{3}{4}} \right)} + i \sin{\left(2^{\frac{3}{4}} \right)}\right) 
=
                     / 3/4\      3/4
           / 3/4\    \2   /    -2   
-12 + 2*cos\2   / + e       + e
−12+2cos⁡(234)+e−234+e234-12 + 2 \cos{\left(2^{\frac{3}{4}} \right)} + e^{- 2^{\frac{3}{4}}} + e^{2^{\frac{3}{4}}} 
producto
/        3/4\ /      / 3/4\\                                                              
|      -2   | |      \2   /| /          / 3/4\      / 3/4\\ /          / 3/4\      / 3/4\\
\-3 + e     /*\-3 + e      /*\-3 - I*sin\2   / + cos\2   //*\-3 + I*sin\2   / + cos\2   //
(−3+e−234)(−3+e234)(−3+cos⁡(234)−isin⁡(234))(−3+cos⁡(234)+isin⁡(234))\left(-3 + e^{- 2^{\frac{3}{4}}}\right) \left(-3 + e^{2^{\frac{3}{4}}}\right) \left(-3 + \cos{\left(2^{\frac{3}{4}} \right)} - i \sin{\left(2^{\frac{3}{4}} \right)}\right) \left(-3 + \cos{\left(2^{\frac{3}{4}} \right)} + i \sin{\left(2^{\frac{3}{4}} \right)}\right) 
=
 /       / 3/4\\ /     / 3/4\\                       3/4
 |       \2   /| |     \2   /| /          / 3/4\\  -2   
-\1 - 3*e      /*\3 - e      /*\10 - 6*cos\2   //*e
−(1−3e234)(3−e234)(10−6cos⁡(234))e234- \frac{\left(1 - 3 e^{2^{\frac{3}{4}}}\right) \left(3 - e^{2^{\frac{3}{4}}}\right) \left(10 - 6 \cos{\left(2^{\frac{3}{4}} \right)}\right)}{e^{2^{\frac{3}{4}}}} 
-(1 - 3*exp(2^(3/4)))*(3 - exp(2^(3/4)))*(10 - 6*cos(2^(3/4)))*exp(-2^(3/4))
Respuesta numérica [src] 
x1 = -2.81395986156408
x2 = 2.37518413180749
x3 = -3.11076872710895 - 0.993846209981535*i
x4 = -3.11076872710895 + 0.993846209981535*i
x4 = -3.11076872710895 + 0.993846209981535*i
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