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- La ecuación:
- Ecuación x+y-3=0
-
Ecuación x^2=-3
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 3^x=-1
- Expresar {x} en función de y en la ecuación:
- 4*x+8*y=7
- -1*x+4*y=-10
- -14*x-8*y=20
- 11*x-2*y=-9
- Integral de d{x}:
- 0.2
- Suma de la serie:
-
0.2
-
Expresiones idénticas
- log dos cos(x)= cero .2
- logaritmo de 2 coseno de (x) es igual a 0.2
- logaritmo de dos coseno de (x) es igual a cero .2
- log2cosx=0.2
- log2cos(x)=O.2
-
Expresiones semejantes
- log(0.)*2*(4*x+7)=-2
- 2(log(2cosx)/log(3))−13(log(2cosx)/log(3))+6=0
- log(2cosx)=2
- log(2cosx)/log3=4
- log2cosx=0.2
log2cos(x)=0.2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(2*cos(x)) = 1/5
$$\log{\left(2 \cos{\left(x \right)} \right)} = \frac{1}{5}$$
Solución detallada
Tenemos la ecuación
$$\log{\left(2 \cos{\left(x \right)} \right)} = \frac{1}{5}$$
cambiamos
$$\log{\left(2 \cos{\left(x \right)} \right)} - \frac{1}{5} = 0$$
$$\log{\left(2 \cos{\left(x \right)} \right)} - \frac{1}{5} = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$\log{\left(2 w \right)} - \frac{1}{5} = 0$$
$$\log{\left(2 w \right)} = \frac{1}{5}$$
Es la ecuación de la forma:
Por definición log
entonces
$$2 w = e^{\frac{1}{5}}$$
simplificamos
$$2 w = e^{\frac{1}{5}}$$
$$w = \frac{e^{\frac{1}{5}}}{2}$$
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:
$$\log{\left(2 \cos{\left(x \right)} \right)} = \frac{1}{5}$$
cambiamos
$$\log{\left(2 \cos{\left(x \right)} \right)} - \frac{1}{5} = 0$$
$$\log{\left(2 \cos{\left(x \right)} \right)} - \frac{1}{5} = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$\log{\left(2 w \right)} - \frac{1}{5} = 0$$
$$\log{\left(2 w \right)} = \frac{1}{5}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$2 w = e^{\frac{1}{5}}$$
simplificamos
$$2 w = e^{\frac{1}{5}}$$
$$w = \frac{e^{\frac{1}{5}}}{2}$$
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
/ 1/5\ / 1/5\
|e | |e |
- acos|----| + 2*pi + acos|----|
\ 2 / \ 2 /
$$\operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)} + \left(- \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
producto
/ / 1/5\ \ / 1/5\ | |e | | |e | |- acos|----| + 2*pi|*acos|----| \ \ 2 / / \ 2 /
$$\left(- \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)}$$
=
/ / 1/5\ \ / 1/5\ | |e | | |e | |- acos|----| + 2*pi|*acos|----| \ \ 2 / / \ 2 /
$$\left(- \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)}$$
(-acos(exp(1/5)/2) + 2*pi)*acos(exp(1/5)/2)
Respuesta rápida
[src]
/ 1/5\
|e |
x1 = - acos|----| + 2*pi
\ 2 /
$$x_{1} = - \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)} + 2 \pi$$
/ 1/5\
|e |
x2 = acos|----|
\ 2 /
$$x_{2} = \operatorname{acos}{\left(\frac{e^{\frac{1}{5}}}{2} \right)}$$
x2 = acos(exp(1/5)/2)
Respuesta numérica
[src]
x1 = 36.7852615401172
x2 = 19.763406224499
x3 = 57.4625180675766
x4 = 24.2188909257581
x5 = -93.3339293047335
x6 = -19.763406224499
x7 = -7.19703561013987
x8 = -55.634817461656
x9 = -95.1616299106541
x10 = -17.9357056185785
x11 = -82.5952592962949
x12 = -11.6525203113989
x13 = -74.4843733831948
x14 = -0.913850302960281
x15 = -51.179332760397
x16 = -38.6129621460378
x17 = -36.7852615401172
x18 = 101.444815217834
x19 = -49.3516321544764
x20 = -80.7675586903743
x21 = 68.2011880760152
x22 = -61.9180027688356
x23 = 82.5952592962949
x24 = 30.5020762329377
x25 = 0.913850302960281
x26 = 76.3120739891153
x27 = -87.0507439975539
x28 = -13.4802209173195
x29 = 32.3297768388582
x30 = -99.6171146119131
x31 = 70.0288886819357
x32 = -68.2011880760152
x33 = -76.3120739891153
x34 = 44.8961474532174
x35 = 49.3516321544764
x36 = 99.6171146119131
x37 = 17.9357056185785
x38 = -44.8961474532174
x39 = -32.3297768388582
x40 = -101.444815217834
x41 = 87.0507439975539
x42 = -5.36933500421931
x43 = 88.8784446034745
x44 = -43.0684468472968
x45 = -30.5020762329377
x46 = 13.4802209173195
x47 = 61.9180027688356
x48 = 80.7675586903743
x49 = 38.6129621460378
x50 = -70.0288886819357
x51 = 11.6525203113989
x52 = -57.4625180675766
x53 = 5.36933500421931
x54 = 7.19703561013987
x55 = 74.4843733831948
x56 = 26.0465915316786
x57 = -26.0465915316786
x58 = 93.3339293047335
x59 = 43.0684468472968
x60 = 63.7457033747561
x61 = -63.7457033747561
x62 = 55.634817461656
x63 = -24.2188909257581
x63 = -24.2188909257581