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La ecuación:
Ecuación x^2+5x=36
Ecuación 3*x=8
Ecuación 9-7(x+3)=5-6x
Ecuación 4x-5=3+2(x+1)
Expresar {x} en función de y en la ecuación:
-17*x+2*y=9
10*x-15*y=16
-17*x+2*y=-4
-2*x-19*y=3
Expresiones idénticas
cuatro ^(x+ cinco)= dieciséis ^(uno -2x)
4 en el grado (x más 5) es igual a 16 en el grado (1 menos 2x)
cuatro en el grado (x más cinco) es igual a dieciséis en el grado (uno menos 2x)
4(x+5)=16(1-2x)
4x+5=161-2x
4^x+5=16^1-2x
Expresiones semejantes
4^(x-5)=16^(1-2x)
4^(x+5)=16^(1+2x)

4^(x+5)=16^(1-2x) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 x + 5     1 - 2*x
4      = 16

$$4^{x + 5} = 16^{1 - 2 x}$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

  3      log(8)      pi*I        log(8)     2*pi*I       log(8)     4*pi*I       log(8)      pi*I        log(8)     2*pi*I       log(8)     4*pi*I      3    3*pi*I      3    3*pi*I      3    pi*I 
- - + - -------- + -------- + - -------- + -------- + - -------- + -------- + - -------- - -------- + - -------- - -------- + - -------- - -------- + - - - -------- + - - + -------- + - - + ------
  5     5*log(2)   5*log(2)     5*log(2)   5*log(2)     5*log(2)   5*log(2)     5*log(2)   5*log(2)     5*log(2)   5*log(2)     5*log(2)   5*log(2)     5   5*log(2)     5   5*log(2)     5   log(2)

$$\left(\left(\left(- \frac{3}{5} - \frac{3 i \pi}{5 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{4 i \pi}{5 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{2 i \pi}{5 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{i \pi}{5 \log{\left(2 \right)}}\right) + \left(\left(\left(- \frac{3}{5} + \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{i \pi}{5 \log{\left(2 \right)}}\right)\right) + \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{2 i \pi}{5 \log{\left(2 \right)}}\right)\right) + \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{4 i \pi}{5 \log{\left(2 \right)}}\right)\right)\right)\right)\right)\right) + \left(- \frac{3}{5} + \frac{3 i \pi}{5 \log{\left(2 \right)}}\right)\right) + \left(- \frac{3}{5} + \frac{i \pi}{\log{\left(2 \right)}}\right)$$

  12   6*log(8)    pi*I 
- -- - -------- + ------
  5    5*log(2)   log(2)

$$- \frac{6 \log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{12}{5} + \frac{i \pi}{\log{\left(2 \right)}}$$

producto

   /   log(8)      pi*I  \                                                                                                                                                                         
-3*|- -------- + --------|                                                                                                                                                                         
   \  5*log(2)   5*log(2)/ /   log(8)     2*pi*I \ /   log(8)     4*pi*I \ /   log(8)      pi*I  \ /   log(8)     2*pi*I \ /   log(8)     4*pi*I \ /  3    3*pi*I \ /  3    3*pi*I \ /  3    pi*I \
--------------------------*|- -------- + --------|*|- -------- + --------|*|- -------- - --------|*|- -------- - --------|*|- -------- - --------|*|- - - --------|*|- - + --------|*|- - + ------|
            5              \  5*log(2)   5*log(2)/ \  5*log(2)   5*log(2)/ \  5*log(2)   5*log(2)/ \  5*log(2)   5*log(2)/ \  5*log(2)   5*log(2)/ \  5   5*log(2)/ \  5   5*log(2)/ \  5   log(2)/

$$- \frac{3 \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{i \pi}{5 \log{\left(2 \right)}}\right)}{5} \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{2 i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{4 i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{2 i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{4 i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{3}{5} - \frac{3 i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{3}{5} + \frac{3 i \pi}{5 \log{\left(2 \right)}}\right) \left(- \frac{3}{5} + \frac{i \pi}{\log{\left(2 \right)}}\right)$$

27*(pi*I + log(2))*(pi*I + log(8))*(-pi*I + log(2))*(-pi*I + log(8))*(-5*pi*I + log(8))*(-4*pi*I + log(8))*(-2*pi*I + log(8))*(2*pi*I + log(8))*(4*pi*I + log(8))
-----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    9                                                                            
                                                                         9765625*log (2)

$$\frac{27 \left(\log{\left(2 \right)} - i \pi\right) \left(\log{\left(2 \right)} + i \pi\right) \left(\log{\left(8 \right)} - 5 i \pi\right) \left(\log{\left(8 \right)} - 4 i \pi\right) \left(\log{\left(8 \right)} - 2 i \pi\right) \left(\log{\left(8 \right)} - i \pi\right) \left(\log{\left(8 \right)} + i \pi\right) \left(\log{\left(8 \right)} + 2 i \pi\right) \left(\log{\left(8 \right)} + 4 i \pi\right)}{9765625 \log{\left(2 \right)}^{9}}$$

27*(pi*i + log(2))*(pi*i + log(8))*(-pi*i + log(2))*(-pi*i + log(8))*(-5*pi*i + log(8))*(-4*pi*i + log(8))*(-2*pi*i + log(8))*(2*pi*i + log(8))*(4*pi*i + log(8))/(9765625*log(2)^9)

Respuesta rápida [src]

x1 = -3/5

$$x_{1} = - \frac{3}{5}$$

        log(8)      pi*I  
x2 = - -------- + --------
       5*log(2)   5*log(2)

$$x_{2} = - \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{i \pi}{5 \log{\left(2 \right)}}$$

        log(8)     2*pi*I 
x3 = - -------- + --------
       5*log(2)   5*log(2)

$$x_{3} = - \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{2 i \pi}{5 \log{\left(2 \right)}}$$

        log(8)     4*pi*I 
x4 = - -------- + --------
       5*log(2)   5*log(2)

$$x_{4} = - \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} + \frac{4 i \pi}{5 \log{\left(2 \right)}}$$

        log(8)      pi*I  
x5 = - -------- - --------
       5*log(2)   5*log(2)

$$x_{5} = - \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{i \pi}{5 \log{\left(2 \right)}}$$

        log(8)     2*pi*I 
x6 = - -------- - --------
       5*log(2)   5*log(2)

$$x_{6} = - \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{2 i \pi}{5 \log{\left(2 \right)}}$$

        log(8)     4*pi*I 
x7 = - -------- - --------
       5*log(2)   5*log(2)

$$x_{7} = - \frac{\log{\left(8 \right)}}{5 \log{\left(2 \right)}} - \frac{4 i \pi}{5 \log{\left(2 \right)}}$$

       3    3*pi*I 
x8 = - - - --------
       5   5*log(2)

$$x_{8} = - \frac{3}{5} - \frac{3 i \pi}{5 \log{\left(2 \right)}}$$

       3    3*pi*I 
x9 = - - + --------
       5   5*log(2)

$$x_{9} = - \frac{3}{5} + \frac{3 i \pi}{5 \log{\left(2 \right)}}$$

        3    pi*I 
x10 = - - + ------
        5   log(2)

$$x_{10} = - \frac{3}{5} + \frac{i \pi}{\log{\left(2 \right)}}$$

x10 = -3/5 + i*pi/log(2)

Respuesta numérica [src]

x1 = -0.6

x2 = -0.6 + 0.906472028365439*i

x3 = -0.6 + 1.81294405673088*i

x4 = -0.6 + 3.62588811346175*i

x5 = -0.6 - 0.906472028365439*i

x6 = -0.6 - 1.81294405673088*i

x7 = -0.6 - 3.62588811346175*i

x8 = -0.6 - 2.71941608509632*i

x9 = -0.6 + 2.71941608509632*i

x10 = -0.6 + 4.53236014182719*i

x10 = -0.6 + 4.53236014182719*i

Gráfico

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Expresiones idénticas

Expresiones semejantes

4^(x+5)=16^(1-2x) la ecuación

Solución numérica:

Solución