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Otras calculadoras
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- La ecuación:
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Ecuación (x+9)^2=36*x
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Ecuación a+120=2000/5
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Ecuación (|x|)=6
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Ecuación 6*x=12
- 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(|7y+ uno |)=-7ln(|x- dos |)
- ln( módulo de 7y más 1|) es igual a menos 7ln(|x menos 2|)
- ln( módulo de 7y más uno |) es igual a menos 7ln(|x menos dos |)
- ln|7y+1|=-7ln|x-2|
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Expresiones semejantes
- ln(|7y-1|)=-7ln(|x-2|)
- ln(|7y+1|)=-7ln(|x+2|)
- ln(|7y+1|)=+7ln(|x-2|)
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Expresiones con funciones
- ln
- ln(-sqrt2*cos(x))=0
- ln(z+1)=pi*i
- ln(x)=4
- ln(u+1)/3-ln(u+4)/3=c+ln(t)/3
- ln(x)=3-2*x
- Módulo |
- |x|=3,2
- |x+3|+|x-2|=7
- |x|=4,5
- |x|=x
- ||x|-2|=2
ln(|7y+1|)=-7ln(|x-2|) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(|7*y + 1|) = -7*log(|x - 2|)
$$\log{\left(\left|{7 y + 1}\right| \right)} = - 7 \log{\left(\left|{x - 2}\right| \right)}$$
Gráfica
Suma y producto de raíces
[src]
suma
// 1 1 \ // 1 1 \ // 1 1 \ // 1 1 \
||2 - ------------- for ------------- > 0| ||2 - ------------- for ------------- > 0| ||2 + ------------- for ------------- >= 0| ||2 + ------------- for ------------- >= 0|
|| |7 _________| |7 _________| | || |7 _________| |7 _________| | || |7 _________| |7 _________| | || |7 _________| |7 _________| |
I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | |
|| | || | || | || |
|| nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise |
\\ / \\ / \\ / \\ /
$$\left(\operatorname{re}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
// 1 1 \ // 1 1 \ // 1 1 \ // 1 1 \
||2 + ------------- for ------------- >= 0| ||2 - ------------- for ------------- > 0| ||2 + ------------- for ------------- >= 0| ||2 - ------------- for ------------- > 0|
|| |7 _________| |7 _________| | || |7 _________| |7 _________| | || |7 _________| |7 _________| | || |7 _________| |7 _________| |
I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | |
|| | || | || | || |
|| nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise |
\\ / \\ / \\ / \\ /
$$\operatorname{re}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
producto
/ // 1 1 \ // 1 1 \\ / // 1 1 \ // 1 1 \\ | ||2 - ------------- for ------------- > 0| ||2 - ------------- for ------------- > 0|| | ||2 + ------------- for ------------- >= 0| ||2 + ------------- for ------------- >= 0|| | || |7 _________| |7 _________| | || |7 _________| |7 _________| || | || |7 _________| |7 _________| | || |7 _________| |7 _________| || |I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | ||*|I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | || | || | || || | || | || || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || \ \\ / \\ // \ \\ / \\ //
$$\left(\operatorname{re}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
/ 2 | |7 _________| |-1 + 4*|\/ 1 + 7*y | 1 |--------------------- for ------------- > 0 < | 2/7| |7 _________| | |(1 + 7*y) | |\/ 1 + 7*y | | | nan otherwise \
$$\begin{cases} \frac{4 \left|{\sqrt[7]{7 y + 1}}\right|^{2} - 1}{\left|{\left(7 y + 1\right)^{\frac{2}{7}}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}$$
Piecewise(((-1 + 4*Abs((1 + 7*y)^(1/7))^2)/Abs((1 + 7*y)^(2/7)), 1/Abs((1 + 7*y)^(1/7)) > 0), (nan, True))
Respuesta rápida
[src]
// 1 1 \ // 1 1 \
||2 - ------------- for ------------- > 0| ||2 - ------------- for ------------- > 0|
|| |7 _________| |7 _________| | || |7 _________| |7 _________| |
x1 = I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{1} = \operatorname{re}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 - \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// 1 1 \ // 1 1 \
||2 + ------------- for ------------- >= 0| ||2 + ------------- for ------------- >= 0|
|| |7 _________| |7 _________| | || |7 _________| |7 _________| |
x2 = I*im|< |\/ 1 + 7*y | |\/ 1 + 7*y | | + re|< |\/ 1 + 7*y | |\/ 1 + 7*y | |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{2} = \operatorname{re}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 2 + \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} & \text{for}\: \frac{1}{\left|{\sqrt[7]{7 y + 1}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
x2 = re(Piecewise((2 + 1/Abs((7*y + 1)^(1/7), 1/Abs((7*y + 1)^(1/7)) >= 0), (nan, True))) + i*im(Piecewise((2 + 1/Abs((7*y + 1)^(1/7)), 1/Abs((7*y + 1)^(1/7)) >= 0), (nan, True))))