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- La ecuación:
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Ecuación x/3+x/4=-21
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Ecuación 3^x=4
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Ecuación 3*x^2=18*x
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Ecuación x^4-8*x^2+7=0
- Expresar {x} en función de y en la ecuación:
- -7*x+15*y=18
- 15*x+7*y=2
- 7*x-2*y=18
- -1*x-6*y=18
-
Expresiones idénticas
- dos (log(2cosx)/log(tres))− trece (log(2cosx)/log(tres))+ seis = cero
- 2( logaritmo de (2 coseno de x) dividir por logaritmo de (3))−13( logaritmo de (2 coseno de x) dividir por logaritmo de (3)) más 6 es igual a 0
- dos ( logaritmo de (2 coseno de x) dividir por logaritmo de (tres))− trece ( logaritmo de (2 coseno de x) dividir por logaritmo de (tres)) más seis es igual a cero
- 2log2cosx/log3−13log2cosx/log3+6=0
- 2(log(2cosx)/log(3))−13(log(2cosx)/log(3))+6=O
- 2(log(2cosx) dividir por log(3))−13(log(2cosx) dividir por log(3))+6=0
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Expresiones semejantes
- 2(log(2cosx)/log(3))−13(log(2cosx)/log(3))-6=0
-
Expresiones con funciones
- Logaritmo log
- log(c)=0
- Log[2,34-2^x]=2-Sqrt[x-4]=0
- log(z)=log(20^(1/2))+(-atan((2)+2*pi*m))*i
- log2x-5log2x=0
- log(x)=x+45*gamma(x)
- Logaritmo log
- log(c)=0
- Log[2,34-2^x]=2-Sqrt[x-4]=0
- log(z)=log(20^(1/2))+(-atan((2)+2*pi*m))*i
- log2x-5log2x=0
- log(x)=x+45*gamma(x)
- Logaritmo log
- log(c)=0
- Log[2,34-2^x]=2-Sqrt[x-4]=0
- log(z)=log(20^(1/2))+(-atan((2)+2*pi*m))*i
- log2x-5log2x=0
- log(x)=x+45*gamma(x)
- Logaritmo log
- log(c)=0
- Log[2,34-2^x]=2-Sqrt[x-4]=0
- log(z)=log(20^(1/2))+(-atan((2)+2*pi*m))*i
- log2x-5log2x=0
- log(x)=x+45*gamma(x)
2(log(2cosx)/log(3))−13(log(2cosx)/log(3))+6=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(2*cos(x)) log(2*cos(x))
2*------------- - 13*------------- + 6 = 0
log(3) log(3)
$$\left(- 13 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} + 2 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}}\right) + 6 = 0$$
Solución detallada
Tenemos la ecuación
$$\left(- 13 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} + 2 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}}\right) + 6 = 0$$
cambiamos
$$\frac{- 11 \log{\left(2 \cos{\left(x \right)} \right)} + \log{\left(729 \right)}}{\log{\left(3 \right)}} = 0$$
$$\left(- 13 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} + 2 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}}\right) + 6 = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$- \frac{11 \log{\left(2 w \right)}}{\log{\left(3 \right)}} + 6 = 0$$
$$- \frac{11 \log{\left(2 w \right)}}{\log{\left(3 \right)}} = -6$$
Devidimos ambás partes de la ecuación por el multiplicador de log =-11/log(3)
$$\log{\left(2 w \right)} = \frac{6 \log{\left(3 \right)}}{11}$$
Es la ecuación de la forma:
Por definición log
entonces
$$2 w = e^{- \frac{6}{\left(-1\right) 11 \frac{1}{\log{\left(3 \right)}}}}$$
simplificamos
$$2 w = 3^{\frac{6}{11}}$$
$$w = \frac{3^{\frac{6}{11}}}{2}$$
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:
$$\left(- 13 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} + 2 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}}\right) + 6 = 0$$
cambiamos
$$\frac{- 11 \log{\left(2 \cos{\left(x \right)} \right)} + \log{\left(729 \right)}}{\log{\left(3 \right)}} = 0$$
$$\left(- 13 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}} + 2 \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{\log{\left(3 \right)}}\right) + 6 = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$- \frac{11 \log{\left(2 w \right)}}{\log{\left(3 \right)}} + 6 = 0$$
$$- \frac{11 \log{\left(2 w \right)}}{\log{\left(3 \right)}} = -6$$
Devidimos ambás partes de la ecuación por el multiplicador de log =-11/log(3)
$$\log{\left(2 w \right)} = \frac{6 \log{\left(3 \right)}}{11}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$2 w = e^{- \frac{6}{\left(-1\right) 11 \frac{1}{\log{\left(3 \right)}}}}$$
simplificamos
$$2 w = 3^{\frac{6}{11}}$$
$$w = \frac{3^{\frac{6}{11}}}{2}$$
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:
Suma y producto de raíces
[src]
suma
/ 6/11\ / 6/11\
|3 | |3 |
- acos|-----| + 2*pi + acos|-----|
\ 2 / \ 2 /
$$\operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)} + \left(- \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
producto
/ / 6/11\ \ / 6/11\ | |3 | | |3 | |- acos|-----| + 2*pi|*acos|-----| \ \ 2 / / \ 2 /
$$\left(- \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)}$$
=
/ / 6/11\ \ / 6/11\ | |3 | | |3 | |- acos|-----| + 2*pi|*acos|-----| \ \ 2 / / \ 2 /
$$\left(- \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)}$$
(-acos(3^(6/11)/2) + 2*pi)*acos(3^(6/11)/2)
Respuesta rápida
[src]
/ 6/11\
|3 |
x1 = - acos|-----| + 2*pi
\ 2 /
$$x_{1} = - \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)} + 2 \pi$$
/ 6/11\
|3 |
x2 = acos|-----|
\ 2 /
$$x_{2} = \operatorname{acos}{\left(\frac{3^{\frac{6}{11}}}{2} \right)}$$
x2 = acos(3^(6/11)/2)
Respuesta numérica
[src]
x1 = 74.9716048260197
x2 = 6.70980416731494
x3 = 87.5379754403789
x4 = -50.692101317572
x5 = 82.10802785347
x6 = 88.3912131606496
x7 = 75.8248425462904
x8 = 63.2584719319312
x9 = -43.5556782901218
x10 = -30.9893076757626
x11 = -0.42661886013535
x12 = 69.5416572391108
x13 = 12.9929894744945
x14 = -38.1257307032129
x15 = 25.5593600888537
x16 = -49.8388635973013
x17 = 68.6884195188401
x18 = 37.2724929829422
x19 = -56.9752866247516
x20 = -5.85656644704424
x21 = -74.9716048260197
x22 = 38.1257307032129
x23 = 94.6743984678291
x24 = -94.6743984678291
x25 = -88.3912131606496
x26 = -68.6884195188401
x27 = 31.8425453960333
x28 = -81.2547901331993
x29 = 100.104346054738
x30 = 56.1220489044809
x31 = 30.9893076757626
x32 = 18.4229370614034
x33 = 43.5556782901218
x34 = 56.9752866247516
x35 = 5.85656644704424
x36 = 19.2761747816741
x37 = -37.2724929829422
x38 = -12.9929894744945
x39 = 12.1397517542238
x40 = 50.692101317572
x41 = -6.70980416731494
x42 = -31.8425453960333
x43 = 100.957583775009
x44 = 81.2547901331993
x45 = -100.957583775009
x46 = -18.4229370614034
x47 = -75.8248425462904
x48 = -19.2761747816741
x49 = -62.4052342116605
x50 = -100.104346054738
x51 = -12.1397517542238
x52 = -63.2584719319312
x53 = -24.706122368583
x54 = 44.4089160103925
x55 = -25.5593600888537
x56 = -56.1220489044809
x57 = -93.8211607475585
x58 = -69.5416572391108
x59 = -44.4089160103925
x60 = 62.4052342116605
x61 = 49.8388635973013
x62 = 93.8211607475585
x63 = 0.42661886013535
x64 = -82.10802785347
x65 = -87.5379754403789
x66 = 24.706122368583
x66 = 24.706122368583