Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x=8
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
- 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
- Integral de d{x}:
- log(x)
- Límite de la función:
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log(x)
- Derivada de:
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log(x)
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Expresiones idénticas
- log(x)=log(sqrt(y^ dos + uno)+ uno)
- logaritmo de (x) es igual a logaritmo de ( raíz cuadrada de (y al cuadrado más 1) más 1)
- logaritmo de (x) es igual a logaritmo de ( raíz cuadrada de (y en el grado dos más uno) más uno)
- log(x)=log(√(y^2+1)+1)
- log(x)=log(sqrt(y2+1)+1)
- logx=logsqrty2+1+1
- log(x)=log(sqrt(y²+1)+1)
- log(x)=log(sqrt(y en el grado 2+1)+1)
- logx=logsqrty^2+1+1
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Expresiones semejantes
- log(x)=log(sqrt(y^2+1)-1)
- -log(y)/2=Const-log(x-1)
- log(x)=log(sqrt(y^2-1)+1)
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Expresiones con funciones
- Logaritmo log
- log(5,x^(2*y))+log(e,(x+y)^5)=17
- log(x^2-x-3)=log(x)
- log(y)-3+4/y=0
- log2(2𝑥−3)=4
- log(y)=-x^2/4
- Logaritmo log
- log(5,x^(2*y))+log(e,(x+y)^5)=17
- log(x^2-x-3)=log(x)
- log(y)-3+4/y=0
- log2(2𝑥−3)=4
- log(y)=-x^2/4
- Raíz cuadrada sqrt
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
- sqrt(3*x+1)=x-1
log(x)=log(sqrt(y^2+1)+1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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log(x) = log\\/ y + 1 + 1/
$$\log{\left(x \right)} = \log{\left(\sqrt{y^{2} + 1} + 1 \right)}$$
Solución detallada
Tenemos la ecuación
$$\log{\left(x \right)} = \log{\left(\sqrt{y^{2} + 1} + 1 \right)}$$
$$\log{\left(x \right)} = \log{\left(\sqrt{y^{2} + 1} + 1 \right)}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x = e^{\frac{\log{\left(\sqrt{y^{2} + 1} + 1 \right)}}{1}}$$
simplificamos
$$x = \sqrt{y^{2} + 1} + 1$$
$$\log{\left(x \right)} = \log{\left(\sqrt{y^{2} + 1} + 1 \right)}$$
$$\log{\left(x \right)} = \log{\left(\sqrt{y^{2} + 1} + 1 \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x = e^{\frac{\log{\left(\sqrt{y^{2} + 1} + 1 \right)}}{1}}$$
simplificamos
$$x = \sqrt{y^{2} + 1} + 1$$
Gráfica
Respuesta rápida
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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 + \/ \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 /
$$x_{1} = i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + 1$$
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) + 1)
Suma y producto de raíces
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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 + \/ \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 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + 1$$
=
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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 + \/ \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 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + 1$$
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 + \/ \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 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + 1$$
=
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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 + \/ \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 /
$$i \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)} + 1$$
1 + ((1 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)^(1/4)*cos(atan2(2*im(y)*re(y), 1 + re(y)^2 - im(y)^2)/2) + i*((1 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)^(1/4)*sin(atan2(2*im(y)*re(y), 1 + re(y)^2 - im(y)^2)/2)