Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2+4*x-32=0
-
Ecuación 9*x^2=0
-
Ecuación 4*x=24+x
-
Ecuación 16-7(5-x)=9
- Expresar {x} en función de y en la ecuación:
- 15*x-5*y=-5
- 16*x-15*y=4
- -5*x+6*y=-8
- 8*x-16*y=14
-
Expresiones idénticas
- log(2cosx)/log3= cuatro
- logaritmo de (2 coseno de x) dividir por logaritmo de 3 es igual a 4
- logaritmo de (2 coseno de x) dividir por logaritmo de 3 es igual a cuatro
- log2cosx/log3=4
- log(2cosx) dividir por log3=4
-
Expresiones semejantes
- 2(log(2cosx)/log(3))−13(log(2cosx)/log(3))+6=0
-
Expresiones con funciones
- Logaritmo log
- log(x^3-2x^2-2x+6)=log(x^3-4x^2-6x+1)
- log^8(-2-x)=2
- log(2cosx)=2
- log2(4^x+a)=x
- log(x)=-5.5
log(2cosx)/log3=4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(2*cos(x))
------------- = 4
log(3)
$$\frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} = 4$$
Solución detallada
Tenemos la ecuación
$$\frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} = 4$$
cambiamos
$$\frac{\log{\left(\frac{2 \cos{\left(x \right)}}{81} \right)}}{\log{\left(3 \right)}} = 0$$
$$\frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} - 4 = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$\frac{\log{\left(2 w \right)}}{\log{\left(3 \right)}} - 4 = 0$$
$$\frac{\log{\left(2 w \right)}}{\log{\left(3 \right)}} = 4$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/log(3)
$$\log{\left(2 w \right)} = 4 \log{\left(3 \right)}$$
Es la ecuación de la forma:
Por definición log
entonces
$$2 w = e^{\frac{4}{\frac{1}{\log{\left(3 \right)}}}}$$
simplificamos
$$2 w = 81$$
$$w = \frac{81}{2}$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
$$\frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} = 4$$
cambiamos
$$\frac{\log{\left(\frac{2 \cos{\left(x \right)}}{81} \right)}}{\log{\left(3 \right)}} = 0$$
$$\frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} - 4 = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$\frac{\log{\left(2 w \right)}}{\log{\left(3 \right)}} - 4 = 0$$
$$\frac{\log{\left(2 w \right)}}{\log{\left(3 \right)}} = 4$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/log(3)
$$\log{\left(2 w \right)} = 4 \log{\left(3 \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$2 w = e^{\frac{4}{\frac{1}{\log{\left(3 \right)}}}}$$
simplificamos
$$2 w = 81$$
$$w = \frac{81}{2}$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
Respuesta rápida
[src]
x1 = 2*pi - I*im(acos(81/2))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}$$
x2 = I*im(acos(81/2)) + re(acos(81/2))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}$$
x2 = re(acos(81/2)) + i*im(acos(81/2))
Suma y producto de raíces
[src]
suma
2*pi - I*im(acos(81/2)) + I*im(acos(81/2)) + re(acos(81/2))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}\right)$$
=
2*pi + re(acos(81/2))
$$\operatorname{re}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)} + 2 \pi$$
producto
(2*pi - I*im(acos(81/2)))*(I*im(acos(81/2)) + re(acos(81/2)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}\right)$$
=
(2*pi - I*im(acos(81/2)))*(I*im(acos(81/2)) + re(acos(81/2)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{81}{2} \right)}\right)}\right)$$
(2*pi - i*im(acos(81/2)))*(i*im(acos(81/2)) + re(acos(81/2)))
Respuesta numérica
[src]
x1 = -56.5486677646163 + 4.3942967040245*i
x2 = -150.79644737231 + 4.3942967040245*i
x3 = 31.4159265358979 - 4.3942967040245*i
x4 = -12.5663706143592 - 4.3942967040245*i
x5 = 87.9645943005142 + 4.3942967040245*i
x6 = 56.5486677646163 + 4.3942967040245*i
x7 = 75.398223686155 + 4.3942967040245*i
x8 = 8.11021064103792e-36 + 4.3942967040245*i
x9 = 62.8318530717959 - 4.3942967040245*i
x10 = 37.6991118430775 - 4.3942967040245*i
x11 = -94.2477796076938 - 4.3942967040245*i
x12 = -56.5486677646163 - 4.3942967040245*i
x13 = 50.2654824574367 + 4.3942967040245*i
x14 = -43.9822971502571 - 4.3942967040245*i
x15 = -37.6991118430775 + 4.3942967040245*i
x16 = -6.28318530717959 + 4.3942967040245*i
x17 = -94.2477796076938 + 4.3942967040245*i
x18 = 56.5486677646163 - 4.3942967040245*i
x19 = -81.6814089933346 + 4.3942967040245*i
x20 = -43.9822971502571 + 4.3942967040245*i
x21 = -12.5663706143592 + 4.3942967040245*i
x22 = 69.1150383789755 - 4.3942967040245*i
x23 = -18.8495559215388 + 4.3942967040245*i
x24 = -25.1327412287183 - 4.3942967040245*i
x25 = 43.9822971502571 + 4.3942967040245*i
x26 = -1514.24765903028 + 4.3942967040245*i
x27 = 1225.22113490002 + 4.3942967040245*i
x28 = 81.6814089933346 + 4.3942967040245*i
x29 = 25.1327412287183 + 4.3942967040245*i
x30 = 100.530964914873 + 4.3942967040245*i
x31 = 50.2654824574367 - 4.3942967040245*i
x32 = -125.663706143592 + 4.3942967040245*i
x33 = 6.28318530717959 + 4.3942967040245*i
x34 = 94.2477796076938 - 4.3942967040245*i
x35 = -37.6991118430775 - 4.3942967040245*i
x36 = 31.4159265358979 + 4.3942967040245*i
x37 = -81.6814089933346 - 4.3942967040245*i
x38 = -50.2654824574367 - 4.3942967040245*i
x39 = -31.4159265358979 - 4.3942967040245*i
x40 = 100.530964914873 - 4.3942967040245*i
x41 = -75.398223686155 - 4.3942967040245*i
x42 = -50.2654824574367 + 4.3942967040245*i
x43 = 18.8495559215388 + 4.3942967040245*i
x44 = -31.4159265358979 + 4.3942967040245*i
x45 = 2.9982965206586e-32 - 4.3942967040245*i
x46 = 94.2477796076938 + 4.3942967040245*i
x47 = 3166.72539481851 - 4.3942967040245*i
x48 = 18.8495559215388 - 4.3942967040245*i
x49 = 12.5663706143592 - 4.3942967040245*i
x50 = -18.8495559215388 - 4.3942967040245*i
x51 = -69.1150383789755 + 4.3942967040245*i
x52 = -100.530964914873 + 4.3942967040245*i
x53 = 6.28318530717959 - 4.3942967040245*i
x54 = 62.8318530717959 + 4.3942967040245*i
x55 = -11755.839709733 + 4.3942967040245*i
x56 = 25.1327412287183 - 4.3942967040245*i
x57 = 37.6991118430775 + 4.3942967040245*i
x58 = 7554636800.10092 - 4.3942967040245*i
x59 = -87.9645943005142 - 4.3942967040245*i
x60 = 43.9822971502571 - 4.3942967040245*i
x61 = -69.1150383789755 - 4.3942967040245*i
x62 = -62.8318530717959 - 4.3942967040245*i
x63 = -25.1327412287183 + 4.3942967040245*i
x64 = -75.398223686155 + 4.3942967040245*i
x65 = 69.1150383789755 + 4.3942967040245*i
x66 = -87.9645943005142 + 4.3942967040245*i
x67 = 169.646003293849 - 4.3942967040245*i
x68 = 12.5663706143592 + 4.3942967040245*i
x69 = -62.8318530717959 + 4.3942967040245*i
x70 = 81.6814089933346 - 4.3942967040245*i
x71 = -6.28318530717959 - 4.3942967040245*i
x72 = 87.9645943005142 - 4.3942967040245*i
x72 = 87.9645943005142 - 4.3942967040245*i