Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
- Ecuación x^2-49=0
-
Ecuación 1-x/2=x/3
-
Ecuación 3*x^2-9=0
-
Ecuación -8x-17=3x-105
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -19*x+14*y=20
- 5*x-14*y=-15
-
Expresiones idénticas
- log(sinx) uno = dos
- logaritmo de ( seno de x)1 es igual a 2
- logaritmo de ( seno de x) uno es igual a dos
- logsinx1=2
-
Expresiones con funciones
- Logaritmo log
- log2x+2(25)=2
- log(1/2)*x=2*x+5
- log(2*y+1)/2=log(sin(x))
- log(1)/x*x^2=-1
- log(x+1)((x-1)(x^2+x-8))=log(x-1)((x+1)^3)
- sinx
- sinx+sin3x=2sin2x
- sinx+tgx=sin2x
- sinx+x^2cosy-y^2=0
- sinx/2(cos2x+1)=0
- sinx-0,2x=0
log(sinx)1=2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\log{\left(\sin{\left(x \right)} \right)} = 2$$
cambiamos
$$\log{\left(\sin{\left(x \right)} \right)} - 2 = 0$$
$$\log{\left(\sin{\left(x \right)} \right)} - 2 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Tenemos la ecuación
$$\log{\left(w \right)} - 2 = 0$$
$$\log{\left(w \right)} = 2$$
Es la ecuación de la forma:
Por definición log
entonces
$$w = e^{\frac{2}{1}}$$
simplificamos
$$w = e^{2}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$\log{\left(\sin{\left(x \right)} \right)} = 2$$
cambiamos
$$\log{\left(\sin{\left(x \right)} \right)} - 2 = 0$$
$$\log{\left(\sin{\left(x \right)} \right)} - 2 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Tenemos la ecuación
$$\log{\left(w \right)} - 2 = 0$$
$$\log{\left(w \right)} = 2$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$w = e^{\frac{2}{1}}$$
simplificamos
$$w = e^{2}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
Suma y producto de raíces
[src]
suma
/ / 2\\ / / 2\\ / / 2\\ / / 2\\ pi - re\asin\e // - I*im\asin\e // + I*im\asin\e // + re\asin\e //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}\right)$$
=
pi
$$\pi$$
producto
/ / / 2\\ / / 2\\\ / / / 2\\ / / 2\\\ \pi - re\asin\e // - I*im\asin\e ///*\I*im\asin\e // + re\asin\e ///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}\right)$$
=
/ / / 2\\ / / 2\\\ / / / 2\\ / / 2\\\ -\I*im\asin\e // + re\asin\e ///*\-pi + I*im\asin\e // + re\asin\e ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}\right)$$
-(i*im(asin(exp(2))) + re(asin(exp(2))))*(-pi + i*im(asin(exp(2))) + re(asin(exp(2))))
Respuesta rápida
[src]
/ / 2\\ / / 2\\ x1 = pi - re\asin\e // - I*im\asin\e //
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}$$
/ / 2\\ / / 2\\ x2 = I*im\asin\e // + re\asin\e //
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(e^{2} \right)}\right)}$$
x2 = re(asin(exp(2))) + i*im(asin(exp(2)))
Respuesta numérica
[src]
x1 = -73.8274273593601 - 2.68853649730747*i
x2 = 57542.9818394774 + 2.68853649730747*i
x3 = 70.6858347057703 - 2.68853649730747*i
x4 = 64.4026493985908 - 2.68853649730747*i
x5 = 64.4026493985908 + 2.68853649730747*i
x6 = -293.738913110646 - 2.68853649730747*i
x7 = 39.2699081698724 + 2.68853649730747*i
x8 = -86.3937979737193 + 2.68853649730747*i
x9 = 26.7035375555132 - 2.68853649730747*i
x10 = -23.5619449019235 - 2.68853649730747*i
x11 = -29.845130209103 + 2.68853649730747*i
x12 = -23.5619449019235 + 2.68853649730747*i
x13 = -98.9601685880785 + 2.68853649730747*i
x14 = 7.85398163397448 + 2.68853649730747*i
x15 = 89.5353906273091 + 2.68853649730747*i
x16 = -42.4115008234622 + 2.68853649730747*i
x17 = 102.101761241668 - 2.68853649730747*i
x18 = 32.9867228626928 - 2.68853649730747*i
x19 = 14.1371669411541 - 2.68853649730747*i
x20 = 76.9690200129499 + 2.68853649730747*i
x21 = -98.9601685880785 - 2.68853649730747*i
x22 = 83.2522053201295 - 2.68853649730747*i
x23 = -42.4115008234622 - 2.68853649730747*i
x24 = -4.71238898038469 - 2.68853649730747*i
x25 = -10.9955742875643 - 2.68853649730747*i
x26 = 83.2522053201295 + 2.68853649730747*i
x27 = 20.4203522483337 - 2.68853649730747*i
x28 = -17.2787595947439 - 2.68853649730747*i
x29 = -105.243353895258 + 2.68853649730747*i
x30 = -117.809724509617 - 2.68853649730747*i
x31 = -54.9778714378214 + 2.68853649730747*i
x32 = -238131.15234578 - 2.68853649730747*i
x33 = -300648.846152216 - 2.68853649730747*i
x34 = -80.1106126665397 + 2.68853649730747*i
x35 = 14.1371669411541 + 2.68853649730747*i
x36 = 26.7035375555132 + 2.68853649730747*i
x37 = 51.8362787842316 - 2.68853649730747*i
x38 = -15455.065059335 - 2.68853649730747*i
x39 = 45.553093477052 + 2.68853649730747*i
x40 = -54.9778714378214 - 2.68853649730747*i
x41 = 58.1194640914112 + 2.68853649730747*i
x42 = 32.9867228626928 + 2.68853649730747*i
x43 = -23007.4537985648 - 2.68853649730747*i
x44 = -92.6769832808989 - 2.68853649730747*i
x45 = 322.013246992954 + 2.68853649730747*i
x46 = -142.942465738336 + 2.68853649730747*i
x47 = -61.261056745001 + 2.68853649730747*i
x48 = 45.553093477052 - 2.68853649730747*i
x49 = 51.8362787842316 + 2.68853649730747*i
x50 = 2037.32283585298 + 2.68853649730747*i
x51 = 89.5353906273091 - 2.68853649730747*i
x52 = 1.5707963267949 + 2.68853649730747*i
x53 = 554.491103358598 - 2.68853649730747*i
x54 = 1.5707963267949 - 2.68853649730747*i
x55 = 95.8185759344887 + 2.68853649730747*i
x56 = 70.6858347057703 + 2.68853649730747*i
x57 = 20.4203522483337 + 2.68853649730747*i
x58 = -48.6946861306418 - 2.68853649730747*i
x59 = -10.9955742875643 + 2.68853649730747*i
x60 = -36.1283155162826 + 2.68853649730747*i
x61 = 58.1194640914112 - 2.68853649730747*i
x62 = -99656.0313608486 - 2.68853649730747*i
x63 = -36.1283155162826 - 2.68853649730747*i
x64 = -73.8274273593601 + 2.68853649730747*i
x65 = -67.5442420521806 - 2.68853649730747*i
x66 = -17.2787595947439 + 2.68853649730747*i
x67 = -80.1106126665397 - 2.68853649730747*i
x68 = 95.8185759344887 - 2.68853649730747*i
x69 = 39.2699081698724 - 2.68853649730747*i
x70 = 7.85398163397448 - 2.68853649730747*i
x71 = -61.261056745001 - 2.68853649730747*i
x72 = -29.845130209103 - 2.68853649730747*i
x73 = -940.906999750143 - 2.68853649730747*i
x74 = -67.5442420521806 + 2.68853649730747*i
x74 = -67.5442420521806 + 2.68853649730747*i