Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
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Ecuación x-x/7=15/7
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Ecuación (x-7)^2=(9-x)^2
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Ecuación 1-2*(5-2*x)=-x-3
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Ecuación x^3+4*x^2-x-4=0
- Expresar {x} en función de y en la ecuación:
- -16*x-7*y=-5
- 17*x-11*y=2
- 7*x+19*y=12
- -5*x+5*y=-9
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Expresiones idénticas
- log(y- dos)=Const+log(x)-log(x+ uno / dos)
- logaritmo de (y menos 2) es igual a Const más logaritmo de (x) menos logaritmo de (x más 1 dividir por 2)
- logaritmo de (y menos dos) es igual a Const más logaritmo de (x) menos logaritmo de (x más uno dividir por dos)
- logy-2=Const+logx-logx+1/2
- log(y-2)=Const+log(x)-log(x+1 dividir por 2)
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Expresiones semejantes
- log(y+2)=Const+log(x)-log(x+1/2)
- log(y-2)=Const+log(x)+log(x+1/2)
- log(y-2)=Const-log(x)-log(x+1/2)
- log(y-2)=Const+log(x)-log(x-1/2)
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Expresiones con funciones
- Logaritmo log
- log(4+x)=log(2-x)+2
- log(x)=-2
- log(x)/sqrt(x)=0
- log2(4-x)=7
- log2(4)+log2(x-1)=5
- Logaritmo log
- log(4+x)=log(2-x)+2
- log(x)=-2
- log(x)/sqrt(x)=0
- log2(4-x)=7
- log2(4)+log2(x-1)=5
- Logaritmo log
- log(4+x)=log(2-x)+2
- log(x)=-2
- log(x)/sqrt(x)=0
- log2(4-x)=7
- log2(4)+log2(x-1)=5
log(y-2)=Const+log(x)-log(x+1/2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(y - 2) = c + log(x) - log(x + 1/2)
$$\log{\left(y - 2 \right)} = \left(c + \log{\left(x \right)}\right) - \log{\left(x + \frac{1}{2} \right)}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / re(y)\ / re(c) \ \ / re(y)\ / re(c)\ | |-1 + -----|*\- e *sin(im(c)) + im(y)/ / re(c)\ | |-1 + -----|*\2 - re(y) + cos(im(c))*e / / re(c) \ | \ 2 / \2 - re(y) + cos(im(c))*e /*im(y) | \ 2 / \- e *sin(im(c)) + im(y)/*im(y) I*|---------------------------------------------------------------- + --------------------------------------------------------------------| + ---------------------------------------------------------------- - -------------------------------------------------------------------- | 2 2 / 2 2\| 2 2 / 2 2\ |/ re(c) \ / re(c)\ |/ re(c) \ / re(c)\ || / re(c) \ / re(c)\ |/ re(c) \ / re(c)\ | \\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / // \-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / /
$$- \frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)} + i \left(\frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)}\right) + \frac{\left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}}$$
=
/ / re(y)\ / re(c) \ \ / re(y)\ / re(c)\ | |-1 + -----|*\- e *sin(im(c)) + im(y)/ / re(c)\ | |-1 + -----|*\2 - re(y) + cos(im(c))*e / / re(c) \ | \ 2 / \2 - re(y) + cos(im(c))*e /*im(y) | \ 2 / \- e *sin(im(c)) + im(y)/*im(y) I*|---------------------------------------------------------------- + --------------------------------------------------------------------| + ---------------------------------------------------------------- - -------------------------------------------------------------------- | 2 2 / 2 2\| 2 2 / 2 2\ |/ re(c) \ / re(c)\ |/ re(c) \ / re(c)\ || / re(c) \ / re(c)\ |/ re(c) \ / re(c)\ | \\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / // \-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / /
$$- \frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)} + i \left(\frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)}\right) + \frac{\left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}}$$
producto
/ / re(y)\ / re(c) \ \ / re(y)\ / re(c)\ | |-1 + -----|*\- e *sin(im(c)) + im(y)/ / re(c)\ | |-1 + -----|*\2 - re(y) + cos(im(c))*e / / re(c) \ | \ 2 / \2 - re(y) + cos(im(c))*e /*im(y) | \ 2 / \- e *sin(im(c)) + im(y)/*im(y) I*|---------------------------------------------------------------- + --------------------------------------------------------------------| + ---------------------------------------------------------------- - -------------------------------------------------------------------- | 2 2 / 2 2\| 2 2 / 2 2\ |/ re(c) \ / re(c)\ |/ re(c) \ / re(c)\ || / re(c) \ / re(c)\ |/ re(c) \ / re(c)\ | \\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / // \-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / /
$$- \frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)} + i \left(\frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)}\right) + \frac{\left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}}$$
=
/ / re(c) \ / re(c)\ \ / re(c)\ / re(c) \
I*\(2 - re(y))*\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e /*im(y)/ + (-2 + re(y))*\2 - re(y) + cos(im(c))*e / + \-im(y) + e *sin(im(c))/*im(y)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 2\
|/ re(c) \ / re(c)\ |
2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / /
$$\frac{i \left(\left(2 - \operatorname{re}{\left(y\right)}\right) \left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right) + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right) \operatorname{im}{\left(y\right)}\right) + \left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} + \left(\operatorname{re}{\left(y\right)} - 2\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)}$$
(i*((2 - re(y))*(-im(y) + exp(re(c))*sin(im(c))) + (2 - re(y) + cos(im(c))*exp(re(c)))*im(y)) + (-2 + re(y))*(2 - re(y) + cos(im(c))*exp(re(c))) + (-im(y) + exp(re(c))*sin(im(c)))*im(y))/(2*((-im(y) + exp(re(c))*sin(im(c)))^2 + (2 - re(y) + cos(im(c))*exp(re(c)))^2))
Respuesta rápida
[src]
/ / re(y)\ / re(c) \ \ / re(y)\ / re(c)\
| |-1 + -----|*\- e *sin(im(c)) + im(y)/ / re(c)\ | |-1 + -----|*\2 - re(y) + cos(im(c))*e / / re(c) \
| \ 2 / \2 - re(y) + cos(im(c))*e /*im(y) | \ 2 / \- e *sin(im(c)) + im(y)/*im(y)
x1 = I*|---------------------------------------------------------------- + --------------------------------------------------------------------| + ---------------------------------------------------------------- - --------------------------------------------------------------------
| 2 2 / 2 2\| 2 2 / 2 2\
|/ re(c) \ / re(c)\ |/ re(c) \ / re(c)\ || / re(c) \ / re(c)\ |/ re(c) \ / re(c)\ |
\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / // \-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / 2*\\-im(y) + e *sin(im(c))/ + \2 - re(y) + cos(im(c))*e / /
$$x_{1} = - \frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)} + i \left(\frac{\left(- e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \operatorname{im}{\left(y\right)}\right) \left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right) \operatorname{im}{\left(y\right)}}{2 \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}\right)}\right) + \frac{\left(\frac{\operatorname{re}{\left(y\right)}}{2} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)}{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(y\right)} + 2\right)^{2}}$$
x1 = -(-exp(re(c))*sin(im(c)) + im(y))*im(y)/(2*((exp(re(c))*sin(im(c)) - im(y))^2 + (exp(re(c))*cos(im(c)) - re(y) + 2)^2)) + i*((-exp(re(c))*sin(im(c)) + im(y))*(re(y)/2 - 1)/((exp(re(c))*sin(im(c)) - im(y))^2 + (exp(re(c))*cos(im(c)) - re(y) + 2)^2) + (exp(re(c))*cos(im(c)) - re(y) + 2)*im(y)/(2*((exp(re(c))*sin(im(c)) - im(y))^2 + (exp(re(c))*cos(im(c)) - re(y) + 2)^2))) + (re(y)/2 - 1)*(exp(re(c))*cos(im(c)) - re(y) + 2)/((exp(re(c))*sin(im(c)) - im(y))^2 + (exp(re(c))*cos(im(c)) - re(y) + 2)^2)