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Otras calculadoras
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- La ecuación:
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Ecuación x+(x/4)=-5
- Ecuación z^4-81=0
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Ecuación z^3=8
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Ecuación x^3+x^2-2=0
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
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Expresiones idénticas
- log(y- uno)/ dos -log(y+ uno)/ dos =c+log(x)- uno /x
- logaritmo de (y menos 1) dividir por 2 menos logaritmo de (y más 1) dividir por 2 es igual a c más logaritmo de (x) menos 1 dividir por x
- logaritmo de (y menos uno) dividir por dos menos logaritmo de (y más uno) dividir por dos es igual a c más logaritmo de (x) menos uno dividir por x
- logy-1/2-logy+1/2=c+logx-1/x
- log(y-1) dividir por 2-log(y+1) dividir por 2=c+log(x)-1 dividir por x
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Expresiones semejantes
- log(y+1)/2-log(y+1)/2=c+log(x)-1/x
- log(y-1)/2-log(y-1)/2=c+log(x)-1/x
- log(y-1)/2+log(y+1)/2=c+log(x)-1/x
- log(y-1)/2-log(y+1)/2=c-log(x)-1/x
- log(y-1)/2-log(y+1)/2=c+log(x)+1/x
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Expresiones con funciones
- Logaritmo log
- log(2)/log(x)-log(3)/log(x)=4
- log4(x^2+x-25)=-log4(1/x)
- log_x-6(x^2-12)=2
- Log2-x(x2+3x-6)=1.
- log3(x-1)=-2
- Logaritmo log
- log(2)/log(x)-log(3)/log(x)=4
- log4(x^2+x-25)=-log4(1/x)
- log_x-6(x^2-12)=2
- Log2-x(x2+3x-6)=1.
- log3(x-1)=-2
- Logaritmo log
- log(2)/log(x)-log(3)/log(x)=4
- log4(x^2+x-25)=-log4(1/x)
- log_x-6(x^2-12)=2
- Log2-x(x2+3x-6)=1.
- log3(x-1)=-2
log(y-1)/2-log(y+1)/2=c+log(x)-1/x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(y - 1) log(y + 1) 1
---------- - ---------- = c + log(x) - -
2 2 x
$$\frac{\log{\left(y - 1 \right)}}{2} - \frac{\log{\left(y + 1 \right)}}{2} = \left(c + \log{\left(x \right)}\right) - \frac{1}{x}$$
Gráfica
Respuesta rápida
[src]
/ / ______________\\ / / ______________\\
| | / 2*c || | | / 2*c ||
| | / (1 + y)*e || | | / (1 + y)*e ||
| -c + W|- / ------------ || | -c + W|- / ------------ ||
| ________ \ \/ -1 + y /| | ________ \ \/ -1 + y /|
|\/ -1 + y *e | |\/ -1 + y *e |
x1 = I*im|----------------------------------------| + re|----------------------------------------|
| _______ | | _______ |
\ \/ 1 + y / \ \/ 1 + y /
$$x_{1} = \operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}$$
/ / ______________\\ / / ______________\\
| | / 2*c || | | / 2*c ||
| | / (1 + y)*e || | | / (1 + y)*e ||
| -c + W| / ------------ || | -c + W| / ------------ ||
| ________ \\/ -1 + y /| | ________ \\/ -1 + y /|
|\/ -1 + y *e | |\/ -1 + y *e |
x2 = I*im|---------------------------------------| + re|---------------------------------------|
| _______ | | _______ |
\ \/ 1 + y / \ \/ 1 + y /
$$x_{2} = \operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}$$
x2 = re(sqrt(y - 1)*exp(-c + LambertW(sqrt((y + 1)*exp(2*c)/(y - 1))))/sqrt(y + 1)) + i*im(sqrt(y - 1)*exp(-c + LambertW(sqrt((y + 1)*exp(2*c)/(y - 1))))/sqrt(y + 1))
Suma y producto de raíces
[src]
suma
/ / ______________\\ / / ______________\\ / / ______________\\ / / ______________\\
| | / 2*c || | | / 2*c || | | / 2*c || | | / 2*c ||
| | / (1 + y)*e || | | / (1 + y)*e || | | / (1 + y)*e || | | / (1 + y)*e ||
| -c + W|- / ------------ || | -c + W|- / ------------ || | -c + W| / ------------ || | -c + W| / ------------ ||
| ________ \ \/ -1 + y /| | ________ \ \/ -1 + y /| | ________ \\/ -1 + y /| | ________ \\/ -1 + y /|
|\/ -1 + y *e | |\/ -1 + y *e | |\/ -1 + y *e | |\/ -1 + y *e |
I*im|----------------------------------------| + re|----------------------------------------| + I*im|---------------------------------------| + re|---------------------------------------|
| _______ | | _______ | | _______ | | _______ |
\ \/ 1 + y / \ \/ 1 + y / \ \/ 1 + y / \ \/ 1 + y /
$$\left(\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}\right) + \left(\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}\right)$$
=
/ / ______________\\ / / ______________\\ / / ______________\\ / / ______________\\
| | / 2*c || | | / 2*c || | | / 2*c || | | / 2*c ||
| | / (1 + y)*e || | | / (1 + y)*e || | | / (1 + y)*e || | | / (1 + y)*e ||
| -c + W| / ------------ || | -c + W|- / ------------ || | -c + W| / ------------ || | -c + W|- / ------------ ||
| ________ \\/ -1 + y /| | ________ \ \/ -1 + y /| | ________ \\/ -1 + y /| | ________ \ \/ -1 + y /|
|\/ -1 + y *e | |\/ -1 + y *e | |\/ -1 + y *e | |\/ -1 + y *e |
I*im|---------------------------------------| + I*im|----------------------------------------| + re|---------------------------------------| + re|----------------------------------------|
| _______ | | _______ | | _______ | | _______ |
\ \/ 1 + y / \ \/ 1 + y / \ \/ 1 + y / \ \/ 1 + y /
$$\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + \operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}$$
producto
/ / / ______________\\ / / ______________\\\ / / / ______________\\ / / ______________\\\ | | | / 2*c || | | / 2*c ||| | | | / 2*c || | | / 2*c ||| | | | / (1 + y)*e || | | / (1 + y)*e ||| | | | / (1 + y)*e || | | / (1 + y)*e ||| | | -c + W|- / ------------ || | -c + W|- / ------------ ||| | | -c + W| / ------------ || | -c + W| / ------------ ||| | | ________ \ \/ -1 + y /| | ________ \ \/ -1 + y /|| | | ________ \\/ -1 + y /| | ________ \\/ -1 + y /|| | |\/ -1 + y *e | |\/ -1 + y *e || | |\/ -1 + y *e | |\/ -1 + y *e || |I*im|----------------------------------------| + re|----------------------------------------||*|I*im|---------------------------------------| + re|---------------------------------------|| | | _______ | | _______ || | | _______ | | _______ || \ \ \/ 1 + y / \ \/ 1 + y // \ \ \/ 1 + y / \ \/ 1 + y //
$$\left(\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}\right) \left(\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}\right)$$
=
/ / / ______________\\ / / ______________\\\ / / / ______________\\ / / ______________\\\ | | | / 2*c || | | / 2*c ||| | | | / 2*c || | | / 2*c ||| | | | / (1 + y)*e || | | / (1 + y)*e ||| | | | / (1 + y)*e || | | / (1 + y)*e ||| | | -c + W| / ------------ || | -c + W| / ------------ ||| | | -c + W|- / ------------ || | -c + W|- / ------------ ||| | | ________ \\/ -1 + y /| | ________ \\/ -1 + y /|| | | ________ \ \/ -1 + y /| | ________ \ \/ -1 + y /|| | |\/ -1 + y *e | |\/ -1 + y *e || | |\/ -1 + y *e | |\/ -1 + y *e || |I*im|---------------------------------------| + re|---------------------------------------||*|I*im|----------------------------------------| + re|----------------------------------------|| | | _______ | | _______ || | | _______ | | _______ || \ \ \/ 1 + y / \ \/ 1 + y // \ \ \/ 1 + y / \ \/ 1 + y //
$$\left(\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(- \sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}\right) \left(\operatorname{re}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)} + i \operatorname{im}{\left(\frac{\sqrt{y - 1} e^{- c + W\left(\sqrt{\frac{\left(y + 1\right) e^{2 c}}{y - 1}}\right)}}{\sqrt{y + 1}}\right)}\right)$$
(i*im(sqrt(-1 + y)*exp(-c + LambertW(sqrt((1 + y)*exp(2*c)/(-1 + y))))/sqrt(1 + y)) + re(sqrt(-1 + y)*exp(-c + LambertW(sqrt((1 + y)*exp(2*c)/(-1 + y))))/sqrt(1 + y)))*(i*im(sqrt(-1 + y)*exp(-c + LambertW(-sqrt((1 + y)*exp(2*c)/(-1 + y))))/sqrt(1 + y)) + re(sqrt(-1 + y)*exp(-c + LambertW(-sqrt((1 + y)*exp(2*c)/(-1 + y))))/sqrt(1 + y)))