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La ecuación:
Ecuación -x/11+x=50/11
Ecuación 12/x=3
Ecuación 6-5(4x-1)=3
Ecuación 13/(x-5)=5/(x-13)
Expresar {x} en función de y en la ecuación:
-1*x+4*y=-10
-11*x-19*y=14
8*x+6*y=20
-11*x-1*y=15
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
Expresiones semejantes
2(log(2cosx)/log(3))−13(log(2cosx)/log(3))-6=0
Expresiones con funciones
Logaritmo log
log^24x−log4x^3+2=0
log(4^x-b,2)=0
log(1/6)*(x-5)=x+1
log(2*x-1)+log(x-9)=2
logax=0
Logaritmo log
log^24x−log4x^3+2=0
log(4^x-b,2)=0
log(1/6)*(x-5)=x+1
log(2*x-1)+log(x-9)=2
logax=0
Logaritmo log
log^24x−log4x^3+2=0
log(4^x-b,2)=0
log(1/6)*(x-5)=x+1
log(2*x-1)+log(x-9)=2
logax=0
Logaritmo log
log^24x−log4x^3+2=0
log(4^x-b,2)=0
log(1/6)*(x-5)=x+1
log(2*x-1)+log(x-9)=2
logax=0

2(log(2cosx)/log(3))−13(log(2cosx)/log(3))+6=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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

Simplificar

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:

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

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:

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

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