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- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x^2+4=5x
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
- Derivada de:
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lnx
- Integral de d{x}:
- lnx
- Desigualdades:
- lnx
-
Expresiones idénticas
- lnx=- tres /y^ dos
- lnx es igual a menos 3 dividir por y al cuadrado
- lnx es igual a menos tres dividir por y en el grado dos
- lnx=-3/y2
- lnx=-3/y²
- lnx=-3/y en el grado 2
- lnx=-3 dividir por y^2
-
Expresiones semejantes
- 0,076=ln(x/3,9*10^(-3))
- lnx=+3/y^2
- log^2(x,2^0,5)=2-(ln(2^0,5))/ln(x)
- x^(1/x)=ln(x)/x
- (x^3-ln(x^(5,5))-25)-(1/(3-x))=0
- ((2*ln(x)-ln^2(x))/x^2)+3=0
lnx=-3/y^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\log{\left(x \right)} = - \frac{3}{y^{2}}$$
$$\log{\left(x \right)} = - \frac{3}{y^{2}}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x = e^{\frac{\left(-1\right) 3 \frac{1}{y^{2}}}{1}}$$
simplificamos
$$x = e^{- \frac{3}{y^{2}}}$$
$$\log{\left(x \right)} = - \frac{3}{y^{2}}$$
$$\log{\left(x \right)} = - \frac{3}{y^{2}}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x = e^{\frac{\left(-1\right) 3 \frac{1}{y^{2}}}{1}}$$
simplificamos
$$x = e^{- \frac{3}{y^{2}}}$$
Gráfica
Suma y producto de raíces
[src]
suma
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
=
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
producto
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
=
/ 2 2 \
3*\im (y) - re (y)/ 6*I*im(y)*re(y)
--------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2
im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y)
e
$$e^{\frac{3 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{6 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}}$$
exp(3*(im(y)^2 - re(y)^2)/(im(y)^4 + re(y)^4 + 2*im(y)^2*re(y)^2) + 6*i*im(y)*re(y)/(im(y)^4 + re(y)^4 + 2*im(y)^2*re(y)^2))
Respuesta rápida
[src]
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
x1 = cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$x_{1} = i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
x1 = i*exp(-3*re(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4) + 3*im(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4))*sin(6*re(y)*im(y)/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4)) + exp(-3*re(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4) + 3*im(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4))*cos(6*re(y)*im(y)/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4))