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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x=8
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Ecuación (x-87)-27=36
- Ecuación (x^2-16)^2+(x^2+x-20)^2=0
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
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Expresiones idénticas
- dos *lnx+ tres *lny= uno
- 2 multiplicar por lnx más 3 multiplicar por lny es igual a 1
- dos multiplicar por lnx más tres multiplicar por lny es igual a uno
- 2lnx+3lny=1
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Expresiones semejantes
- 2*lnx-3*lny=1
- 2lnx+3lny
2*lnx+3*lny=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2*log(x) + 3*log(y) = 1
$$2 \log{\left(x \right)} + 3 \log{\left(y \right)} = 1$$
Solución detallada
Tenemos la ecuación
$$2 \log{\left(x \right)} + 3 \log{\left(y \right)} = 1$$
$$2 \log{\left(x \right)} = 1 - 3 \log{\left(y \right)}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =2
$$\log{\left(x \right)} = \frac{1}{2} - \frac{3 \log{\left(y \right)}}{2}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x = e^{\frac{1 - 3 \log{\left(y \right)}}{2}}$$
simplificamos
$$x = \frac{e^{\frac{1}{2}}}{y^{\frac{3}{2}}}$$
$$2 \log{\left(x \right)} + 3 \log{\left(y \right)} = 1$$
$$2 \log{\left(x \right)} = 1 - 3 \log{\left(y \right)}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =2
$$\log{\left(x \right)} = \frac{1}{2} - \frac{3 \log{\left(y \right)}}{2}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x = e^{\frac{1 - 3 \log{\left(y \right)}}{2}}$$
simplificamos
$$x = \frac{e^{\frac{1}{2}}}{y^{\frac{3}{2}}}$$
Gráfica
Suma y producto de raíces
[src]
suma
/3*atan2(im(y), re(y))\ 1/2 1/2 /3*atan2(im(y), re(y))\
cos|---------------------|*e I*e *sin|---------------------|
\ 2 / \ 2 /
------------------------------- - ---------------------------------
3/4 3/4
/ 2 2 \ / 2 2 \
\im (y) + re (y)/ \im (y) + re (y)/
$$- \frac{i e^{\frac{1}{2}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}} + \frac{e^{\frac{1}{2}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}}$$
=
/3*atan2(im(y), re(y))\ 1/2 1/2 /3*atan2(im(y), re(y))\
cos|---------------------|*e I*e *sin|---------------------|
\ 2 / \ 2 /
------------------------------- - ---------------------------------
3/4 3/4
/ 2 2 \ / 2 2 \
\im (y) + re (y)/ \im (y) + re (y)/
$$- \frac{i e^{\frac{1}{2}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}} + \frac{e^{\frac{1}{2}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}}$$
producto
/3*atan2(im(y), re(y))\ 1/2 1/2 /3*atan2(im(y), re(y))\
cos|---------------------|*e I*e *sin|---------------------|
\ 2 / \ 2 /
------------------------------- - ---------------------------------
3/4 3/4
/ 2 2 \ / 2 2 \
\im (y) + re (y)/ \im (y) + re (y)/
$$- \frac{i e^{\frac{1}{2}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}} + \frac{e^{\frac{1}{2}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}}$$
=
1 3*I*atan2(im(y), re(y))
- - -----------------------
2 2
e
----------------------------
3/4
/ 2 2 \
\im (y) + re (y)/
$$\frac{e^{- \frac{3 i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} + \frac{1}{2}}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}}$$
exp(1/2 - 3*i*atan2(im(y), re(y))/2)/(im(y)^2 + re(y)^2)^(3/4)
Respuesta rápida
[src]
/3*atan2(im(y), re(y))\ 1/2 1/2 /3*atan2(im(y), re(y))\
cos|---------------------|*e I*e *sin|---------------------|
\ 2 / \ 2 /
x1 = ------------------------------- - ---------------------------------
3/4 3/4
/ 2 2 \ / 2 2 \
\im (y) + re (y)/ \im (y) + re (y)/
$$x_{1} = - \frac{i e^{\frac{1}{2}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}} + \frac{e^{\frac{1}{2}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}}}$$
x1 = -i*exp(1/2)*sin(3*atan2(im(y, re(y))/2)/(re(y)^2 + im(y)^2)^(3/4) + exp(1/2)*cos(3*atan2(im(y), re(y))/2)/(re(y)^2 + im(y)^2)^(3/4))