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- La ecuación:
-
Ecuación x^3+3x^2-x-3=0
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Ecuación (x+9)^2=36*x
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Ecuación x^3-6x^2+11x-6=0
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Ecuación a+120=2000/5
- Expresar {x} en función de y en la ecuación:
- -6*x-12*y=9
- 9*x-1*y=17
- 10*x-2*y=11
- 12*x-3*y=-2
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Expresiones idénticas
- ln(u+ uno)/ tres -ln(u+ cuatro)/ tres =c+ln(t)/ tres
- ln(u más 1) dividir por 3 menos ln(u más 4) dividir por 3 es igual a c más ln(t) dividir por 3
- ln(u más uno) dividir por tres menos ln(u más cuatro) dividir por tres es igual a c más ln(t) dividir por tres
- lnu+1/3-lnu+4/3=c+lnt/3
- ln(u+1) dividir por 3-ln(u+4) dividir por 3=c+ln(t) dividir por 3
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Expresiones semejantes
- ln(u+1)/3-ln(u+4)/3=c-ln(t)/3
- ln(u-1)/3-ln(u+4)/3=c+ln(t)/3
- ln(u+1)/3+ln(u+4)/3=c+ln(t)/3
- ln(u+1)/3-ln(u-4)/3=c+ln(t)/3
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Expresiones con funciones
- ln
- ln(2x)=2−3x
- ln*(x+1)*ctg*sqrt(x)=0
- ln(x)=-0,28188
- Ln(x-2)=0
- ln(1+lny)=-lnx
- ln
- ln(2x)=2−3x
- ln*(x+1)*ctg*sqrt(x)=0
- ln(x)=-0,28188
- Ln(x-2)=0
- ln(1+lny)=-lnx
- ln
- ln(2x)=2−3x
- ln*(x+1)*ctg*sqrt(x)=0
- ln(x)=-0,28188
- Ln(x-2)=0
- ln(1+lny)=-lnx
ln(u+1)/3-ln(u+4)/3=c+ln(t)/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(u + 1) log(u + 4) log(t)
---------- - ---------- = c + ------
3 3 3
$$\frac{\log{\left(u + 1 \right)}}{3} - \frac{\log{\left(u + 4 \right)}}{3} = c + \frac{\log{\left(t \right)}}{3}$$
Gráfica
Respuesta rápida
[src]
/ / / 3*c\\ / 3*c\ / / 3*c\\ / 3*c\ \ 2/ 3*c\ / / 3*c\\ / / 3*c\\
| \1 - 4*re\t*e //*im\t*e / 4*\-1 + re\t*e //*im\t*e / | 4*im \t*e / \1 - 4*re\t*e //*\-1 + re\t*e //
u1 = I*|- -------------------------------- - --------------------------------| - -------------------------------- + ------------------------------------
| 2 2 | 2 2
| / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\| / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\
\ \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e // \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e /
$$u_{1} = \frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} + i \left(- \frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}$$
u1 = (1 - 4*re(t*exp(3*c)))*(re(t*exp(3*c)) - 1)/((re(t*exp(3*c)) - 1)^2 + im(t*exp(3*c))^2) + i*(-(1 - 4*re(t*exp(3*c)))*im(t*exp(3*c))/((re(t*exp(3*c)) - 1)^2 + im(t*exp(3*c))^2) - 4*(re(t*exp(3*c)) - 1)*im(t*exp(3*c))/((re(t*exp(3*c)) - 1)^2 + im(t*exp(3*c))^2)) - 4*im(t*exp(3*c))^2/((re(t*exp(3*c)) - 1)^2 + im(t*exp(3*c))^2)
Suma y producto de raíces
[src]
suma
/ / / 3*c\\ / 3*c\ / / 3*c\\ / 3*c\ \ 2/ 3*c\ / / 3*c\\ / / 3*c\\ | \1 - 4*re\t*e //*im\t*e / 4*\-1 + re\t*e //*im\t*e / | 4*im \t*e / \1 - 4*re\t*e //*\-1 + re\t*e // I*|- -------------------------------- - --------------------------------| - -------------------------------- + ------------------------------------ | 2 2 | 2 2 | / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\| / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\ \ \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e // \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e /
$$\frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} + i \left(- \frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}$$
=
/ / / 3*c\\ / 3*c\ / / 3*c\\ / 3*c\ \ 2/ 3*c\ / / 3*c\\ / / 3*c\\ | \1 - 4*re\t*e //*im\t*e / 4*\-1 + re\t*e //*im\t*e / | 4*im \t*e / \1 - 4*re\t*e //*\-1 + re\t*e // I*|- -------------------------------- - --------------------------------| - -------------------------------- + ------------------------------------ | 2 2 | 2 2 | / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\| / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\ \ \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e // \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e /
$$\frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} + i \left(- \frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}$$
producto
/ / / 3*c\\ / 3*c\ / / 3*c\\ / 3*c\ \ 2/ 3*c\ / / 3*c\\ / / 3*c\\ | \1 - 4*re\t*e //*im\t*e / 4*\-1 + re\t*e //*im\t*e / | 4*im \t*e / \1 - 4*re\t*e //*\-1 + re\t*e // I*|- -------------------------------- - --------------------------------| - -------------------------------- + ------------------------------------ | 2 2 | 2 2 | / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\| / / 3*c\\ 2/ 3*c\ / / 3*c\\ 2/ 3*c\ \ \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e // \-1 + re\t*e // + im \t*e / \-1 + re\t*e // + im \t*e /
$$\frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} + i \left(- \frac{\left(1 - 4 \operatorname{re}{\left(t e^{3 c}\right)}\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right) \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}$$
=
2/ 3*c\ / / 3*c\\ / / 3*c\\ / 3*c\
- 4*im \t*e / - \-1 + 4*re\t*e //*\-1 + re\t*e // + 3*I*im\t*e /
------------------------------------------------------------------------
2
/ / 3*c\\ 2/ 3*c\
\-1 + re\t*e // + im \t*e /
$$\frac{- \left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right) \left(4 \operatorname{re}{\left(t e^{3 c}\right)} - 1\right) - 4 \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2} + 3 i \operatorname{im}{\left(t e^{3 c}\right)}}{\left(\operatorname{re}{\left(t e^{3 c}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(t e^{3 c}\right)}\right)^{2}}$$
(-4*im(t*exp(3*c))^2 - (-1 + 4*re(t*exp(3*c)))*(-1 + re(t*exp(3*c))) + 3*i*im(t*exp(3*c)))/((-1 + re(t*exp(3*c)))^2 + im(t*exp(3*c))^2)