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Otras calculadoras
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- La ecuación:
-
Ecuación x^4+2*x^2-8=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
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Expresiones idénticas
- log(sin(y))=Const+log(x^ dos - dos)/ dos
- logaritmo de ( seno de (y)) es igual a Const más logaritmo de (x al cuadrado menos 2) dividir por 2
- logaritmo de ( seno de (y)) es igual a Const más logaritmo de (x en el grado dos menos dos) dividir por dos
- log(sin(y))=Const+log(x2-2)/2
- logsiny=Const+logx2-2/2
- log(sin(y))=Const+log(x²-2)/2
- log(sin(y))=Const+log(x en el grado 2-2)/2
- logsiny=Const+logx^2-2/2
- log(sin(y))=Const+log(x^2-2) dividir por 2
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Expresiones semejantes
- log(sin(y))=Const-log(x^2-2)/2
- log(sin(y))=Const+log(x^2+2)/2
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Expresiones con funciones
- Logaritmo log
- log(x)=x
- log(2*y+1)/2=c+log(sin(x))
- log(2*x)=0
- log3x=-1
- log1/2(2x-6)=-2
- Seno sin
- sin(x)=1,5
- sin(x-1)=0
- sin2x=1
- sin(3*x)=-1/2
- sin(3*x)=-1
- Logaritmo log
- log(x)=x
- log(2*y+1)/2=c+log(sin(x))
- log(2*x)=0
- log3x=-1
- log1/2(2x-6)=-2
log(sin(y))=Const+log(x^2-2)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \
log\x - 2/
log(sin(y)) = c + -----------
2
$$\log{\left(\sin{\left(y \right)} \right)} = c + \frac{\log{\left(x^{2} - 2 \right)}}{2}$$
Gráfica
Suma y producto de raíces
[src]
suma
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/ 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\
4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //|
- \/ \2 + re\sin (y)*e // + im \sin (y)*e / *cos|-----------------------------------------------| - I*\/ \2 + re\sin (y)*e // + im \sin (y)*e / *sin|-----------------------------------------------| + \/ \2 + re\sin (y)*e // + im \sin (y)*e / *cos|-----------------------------------------------| + I*\/ \2 + re\sin (y)*e // + im \sin (y)*e / *sin|-----------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ _______________________________________________ _______________________________________________ \ / _______________________________________________ _______________________________________________ \ | / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\| | / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\| | 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //|| |4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //|| |- \/ \2 + re\sin (y)*e // + im \sin (y)*e / *cos|-----------------------------------------------| - I*\/ \2 + re\sin (y)*e // + im \sin (y)*e / *sin|-----------------------------------------------||*|\/ \2 + re\sin (y)*e // + im \sin (y)*e / *cos|-----------------------------------------------| + I*\/ \2 + re\sin (y)*e // + im \sin (y)*e / *sin|-----------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)}\right)$$
=
/ / 2 \ / 2 \\
| |/ 2*I*y\ -2*c -2*I*y| |/ 2*I*y\ -2*c -2*I*y||
_______________________________________________ |-im\\-1 + e / *e *e / re\\-1 + e / *e *e /|
/ 2 I*atan2|----------------------------------, 2 - --------------------------------|
/ / / 2 -2*c\\ 2/ 2 -2*c\ \ 4 4 /
-\/ \2 + re\sin (y)*e // + im \sin (y)*e / *e
$$- \sqrt{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(\left(e^{2 i y} - 1\right)^{2} e^{- 2 c} e^{- 2 i y}\right)}}{4},2 - \frac{\operatorname{re}{\left(\left(e^{2 i y} - 1\right)^{2} e^{- 2 c} e^{- 2 i y}\right)}}{4} \right)}}$$
-sqrt((2 + re(sin(y)^2*exp(-2*c)))^2 + im(sin(y)^2*exp(-2*c))^2)*exp(i*atan2(-im((-1 + exp(2*i*y))^2*exp(-2*c)*exp(-2*i*y))/4, 2 - re((-1 + exp(2*i*y))^2*exp(-2*c)*exp(-2*i*y))/4))
Respuesta rápida
[src]
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/ 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\
4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //|
x1 = - \/ \2 + re\sin (y)*e // + im \sin (y)*e / *cos|-----------------------------------------------| - I*\/ \2 + re\sin (y)*e // + im \sin (y)*e / *sin|-----------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)}$$
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/ 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\
4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\sin (y)*e /, 2 + re\sin (y)*e //|
x2 = \/ \2 + re\sin (y)*e // + im \sin (y)*e / *cos|-----------------------------------------------| + I*\/ \2 + re\sin (y)*e // + im \sin (y)*e / *sin|-----------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)},\operatorname{re}{\left(e^{- 2 c} \sin^{2}{\left(y \right)}\right)} + 2 \right)}}{2} \right)}$$
x2 = i*((re(exp(-2*c)*sin(y)^2) + 2)^2 + im(exp(-2*c)*sin(y)^2)^2)^(1/4)*sin(atan2(im(exp(-2*c)*sin(y)^2, re(exp(-2*c)*sin(y)^2) + 2)/2) + ((re(exp(-2*c)*sin(y)^2) + 2)^2 + im(exp(-2*c)*sin(y)^2)^2)^(1/4)*cos(atan2(im(exp(-2*c)*sin(y)^2), re(exp(-2*c)*sin(y)^2) + 2)/2))