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Otras calculadoras
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- La ecuación:
-
Ecuación 0,2x+2,7=1,4-1,1x
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación 2x-3(x+3)=-5
-
Ecuación 5(x-2)^2=-6x-44
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- 8*x+3*y=4
- 6*x+9*y=-9
- Derivada de:
-
2ln(x)
- Integral de d{x}:
- 2ln(x)
- ln((y^2)+1)
- Gráfico de la función y =:
- 2ln(x)
-
Expresiones idénticas
- dos ln(x)=ln((y^2)+ uno)
- 2ln(x) es igual a ln((y al cuadrado ) más 1)
- dos ln(x) es igual a ln((y al cuadrado ) más uno)
- 2ln(x)=ln((y2)+1)
- 2lnx=lny2+1
- 2ln(x)=ln((y²)+1)
- 2ln(x)=ln((y en el grado 2)+1)
- 2lnx=lny^2+1
-
Expresiones semejantes
- ((2*ln(x)-ln^2(x))/x^2)+3=0
- 2*lnx-0.5x+1=0
- 2ln(x)=ln((y^2)-1)
- ln(x+2)=2lnx
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Expresiones con funciones
- ln
- ln(y)-1=(y/3)+(2/3)
- lnv-3ln(cosx)=0
- ln(y)=cos(xy)-7
- lncx=-ln(t(e^(2/sqrt(t))))
- lny=(-1/x)+lnc
2ln(x)=ln((y^2)+1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ 2*log(x) = log\y + 1/
$$2 \log{\left(x \right)} = \log{\left(y^{2} + 1 \right)}$$
Solución detallada
Tenemos la ecuación
$$2 \log{\left(x \right)} = \log{\left(y^{2} + 1 \right)}$$
$$2 \log{\left(x \right)} = \log{\left(y^{2} + 1 \right)}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =2
$$\log{\left(x \right)} = \frac{\log{\left(y^{2} + 1 \right)}}{2}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x = e^{\frac{\log{\left(y^{2} + 1 \right)}}{2}}$$
simplificamos
$$x = \sqrt{y^{2} + 1}$$
$$2 \log{\left(x \right)} = \log{\left(y^{2} + 1 \right)}$$
$$2 \log{\left(x \right)} = \log{\left(y^{2} + 1 \right)}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =2
$$\log{\left(x \right)} = \frac{\log{\left(y^{2} + 1 \right)}}{2}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x = e^{\frac{\log{\left(y^{2} + 1 \right)}}{2}}$$
simplificamos
$$x = \sqrt{y^{2} + 1}$$
Gráfica
Respuesta rápida
[src]
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/| 4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/|
x1 = \/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *cos|-----------------------------------------| + I*\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *sin|-----------------------------------------|
\ 2 / \ 2 /
$$x_{1} = i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}$$
x1 = i*((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2)^(1/4)*sin(atan2(2*re(y)*im(y, re(y)^2 - im(y)^2 + 1)/2) + ((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2)^(1/4)*cos(atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 1)/2))
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/| 4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/|
\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *cos|-----------------------------------------| + I*\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *sin|-----------------------------------------|
\ 2 / \ 2 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}$$
=
__________________________________________ __________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/| 4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/|
\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *cos|-----------------------------------------| + I*\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *sin|-----------------------------------------|
\ 2 / \ 2 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}$$
producto
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/| 4 / / 2 2 \ 2 2 |atan2\2*im(y)*re(y), 1 + re (y) - im (y)/|
\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *cos|-----------------------------------------| + I*\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *sin|-----------------------------------------|
\ 2 / \ 2 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}$$
=
/ 2 2 \
__________________________________________ I*atan2\2*im(y)*re(y), 1 + re (y) - im (y)/
/ 2 -------------------------------------------
4 / / 2 2 \ 2 2 2
\/ \1 + re (y) - im (y)/ + 4*im (y)*re (y) *e
$$\sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} e^{\frac{i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2}}$$
((1 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)^(1/4)*exp(i*atan2(2*im(y)*re(y), 1 + re(y)^2 - im(y)^2)/2)