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Otras calculadoras
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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x=8
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Ecuación (x-87)-27=36
- Ecuación (x^2-16)^2+(x^2+x-20)^2=0
- 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
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Expresiones idénticas
- log(y+ uno)=c+log(x^ dos - uno)/ dos
- logaritmo de (y más 1) es igual a c más logaritmo de (x al cuadrado menos 1) dividir por 2
- logaritmo de (y más uno) es igual a c más logaritmo de (x en el grado dos menos uno) dividir por dos
- log(y+1)=c+log(x2-1)/2
- logy+1=c+logx2-1/2
- log(y+1)=c+log(x²-1)/2
- log(y+1)=c+log(x en el grado 2-1)/2
- logy+1=c+logx^2-1/2
- log(y+1)=c+log(x^2-1) dividir por 2
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Expresiones semejantes
- log(y+1)=c+log(x^2+1)/2
- log(y-1)=c+log(x^2-1)/2
- log(y+1)=c-log(x^2-1)/2
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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(x+1)((x-1)(x^2+x-8))=log(x-1)((x+1)^3)
- 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(x+1)((x-1)(x^2+x-8))=log(x-1)((x+1)^3)
log(y+1)=c+log(x^2-1)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \
log\x - 1/
log(y + 1) = c + -----------
2
$$\log{\left(y + 1 \right)} = c + \frac{\log{\left(x^{2} - 1 \right)}}{2}$$
Gráfica
Suma y producto de raíces
[src]
suma
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/ 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\
4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //|
- \/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *cos|-------------------------------------------------| - I*\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *sin|-------------------------------------------------| + \/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *cos|-------------------------------------------------| + I*\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *sin|-------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ _________________________________________________ _________________________________________________ \ / _________________________________________________ _________________________________________________ \ | / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\| | / 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\| | 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //|| |4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //|| |- \/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *cos|-------------------------------------------------| - I*\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *sin|-------------------------------------------------||*|\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *cos|-------------------------------------------------| + I*\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *sin|-------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right)$$
=
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/ 2 / / 2 -2*c\ / 2 -2*c\\
/ / / 2 -2*c\\ 2/ 2 -2*c\ I*atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //
-\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *e
$$- \sqrt{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}$$
-sqrt((1 + re((1 + y)^2*exp(-2*c)))^2 + im((1 + y)^2*exp(-2*c))^2)*exp(i*atan2(im((1 + y)^2*exp(-2*c)), 1 + re((1 + y)^2*exp(-2*c))))
Respuesta rápida
[src]
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/ 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\
4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //|
x1 = - \/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *cos|-------------------------------------------------| - I*\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *sin|-------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}$$
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/ 2 / / / 2 -2*c\ / 2 -2*c\\\ / 2 / / / 2 -2*c\ / 2 -2*c\\\
4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //| 4 / / / 2 -2*c\\ 2/ 2 -2*c\ |atan2\im\(1 + y) *e /, 1 + re\(1 + y) *e //|
x2 = \/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *cos|-------------------------------------------------| + I*\/ \1 + re\(1 + y) *e // + im \(1 + y) *e / *sin|-------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}$$
x2 = i*((re((y + 1)^2*exp(-2*c)) + 1)^2 + im((y + 1)^2*exp(-2*c))^2)^(1/4)*sin(atan2(im((y + 1)^2*exp(-2*c), re((y + 1)^2*exp(-2*c)) + 1)/2) + ((re((y + 1)^2*exp(-2*c)) + 1)^2 + im((y + 1)^2*exp(-2*c))^2)^(1/4)*cos(atan2(im((y + 1)^2*exp(-2*c)), re((y + 1)^2*exp(-2*c)) + 1)/2))