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La ecuación:
Ecuación 3*x^2-x+2=0
Ecuación x^2=-74
Ecuación z^2+z+1=0
Ecuación 90+x-4*10=60
Expresar {x} en función de y en la ecuación:
9*x+14*y=-10
-4*x-8*y=-20
-12*x-10*y=-16
10*x-15*y=16
Expresiones idénticas
log(dos *x+ uno)/ dos =e^c*(y+ uno)
logaritmo de (2 multiplicar por x más 1) dividir por 2 es igual a e en el grado c multiplicar por (y más 1)
logaritmo de (dos multiplicar por x más uno) dividir por dos es igual a e en el grado c multiplicar por (y más uno)
log(2*x+1)/2=ec*(y+1)
log2*x+1/2=ec*y+1
log(2x+1)/2=e^c(y+1)
log(2x+1)/2=ec(y+1)
log2x+1/2=ecy+1
log2x+1/2=e^cy+1
log(2*x+1) dividir por 2=e^c*(y+1)
Expresiones semejantes
log(2*x-1)/2=e^c*(y+1)
log(2*x+1)/2=e^c*(y-1)
Expresiones con funciones
Logaritmo log
log(2,4-x)+log(2,1-2x)=2log(2,3)
log(x+2)/log(3)=27
log(3)*27=x
log(4/(7-x))/log(x^2)=11
log3(2x^2+x)=log3(6)-log3(2)

log(2x+1)/2=e^c(y+1) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

log(2*x + 1)    c        
------------ = E *(y + 1)
     2

\frac{\log{\left(2 x + 1 \right)}}{2} = e^{c} \left(y + 1\right)

Simplificar

Solución detallada

Tenemos la ecuación

\frac{\log{\left(2 x + 1 \right)}}{2} = e^{c} \left(y + 1\right)

\frac{\log{\left(2 x + 1 \right)}}{2} = \left(y + 1\right) e^{c}

Devidimos ambás partes de la ecuación por el multiplicador de log =1/2

\log{\left(2 x + 1 \right)} = 2 \left(y + 1\right) e^{c}

Es la ecuación de la forma:

log(v)=p

Por definición log

v=e^p

entonces

                    c
           (1 + y)*e 
           ----------
              1/2    
2*x + 1 = e

simplificamos

2 x + 1 = e^{2 \left(y + 1\right) e^{c}}

2 x = e^{2 \left(y + 1\right) e^{c}} - 1

x = \frac{e^{2 \left(y + 1\right) e^{c}}}{2} - \frac{1}{2}

Gráfica

Respuesta rápida [src]

                                                                                                           re(c)      re(c)                                  re(c)                          re(c)      re(c)                                  re(c)                                                                                       
              /   re(c)                            re(c)            re(c)                 \  2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)      2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)    /   re(c)                            re(c)            re(c)                 \
       1   cos\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/*e                                                                              I*e                                                                           *sin\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/
x1 = - - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
       2                                                                                 2                                                                                                                                                                2

x_{1} = \frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}

x1 = i*exp(-2*exp(re(c))*sin(im(c))*im(y) + 2*exp(re(c))*cos(im(c))*re(y) + 2*exp(re(c))*cos(im(c)))*sin(2*exp(re(c))*sin(im(c))*re(y) + 2*exp(re(c))*sin(im(c)) + 2*exp(re(c))*cos(im(c))*im(y))/2 + exp(-2*exp(re(c))*sin(im(c))*im(y) + 2*exp(re(c))*cos(im(c))*re(y) + 2*exp(re(c))*cos(im(c)))*cos(2*exp(re(c))*sin(im(c))*re(y) + 2*exp(re(c))*sin(im(c)) + 2*exp(re(c))*cos(im(c))*im(y))/2 - 1/2

Suma y producto de raíces [src]

suma

                                                                                                      re(c)      re(c)                                  re(c)                          re(c)      re(c)                                  re(c)                                                                                       
         /   re(c)                            re(c)            re(c)                 \  2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)      2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)    /   re(c)                            re(c)            re(c)                 \
  1   cos\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/*e                                                                              I*e                                                                           *sin\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/
- - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
  2                                                                                 2                                                                                                                                                                2

\frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}

                                                                                                      re(c)      re(c)                                  re(c)                          re(c)      re(c)                                  re(c)                                                                                       
         /   re(c)                            re(c)            re(c)                 \  2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)      2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)    /   re(c)                            re(c)            re(c)                 \
  1   cos\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/*e                                                                              I*e                                                                           *sin\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/
- - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
  2                                                                                 2                                                                                                                                                                2

\frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}

producto

                                                                                                      re(c)      re(c)                                  re(c)                          re(c)      re(c)                                  re(c)                                                                                       
         /   re(c)                            re(c)            re(c)                 \  2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)      2*cos(im(c))*e      - 2*e     *im(y)*sin(im(c)) + 2*cos(im(c))*e     *re(y)    /   re(c)                            re(c)            re(c)                 \
  1   cos\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/*e                                                                              I*e                                                                           *sin\2*e     *sin(im(c)) + 2*cos(im(c))*e     *im(y) + 2*e     *re(y)*sin(im(c))/
- - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
  2                                                                                 2                                                                                                                                                                2

\frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}

                                                                                                                              re(c)                                                            re(c)                                                                 
         /                                                      re(c)\  2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*e           2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*e         /                                                      re(c)\
  1   cos\2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*e     /*e                                                              I*e                                                           *sin\2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*e     /
- - + ----------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------
  2                                                                 2                                                                                                                                2

\frac{i e^{2 \left(- \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)}\right) e^{\operatorname{re}{\left(c\right)}}} \sin{\left(2 \left(\sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) e^{\operatorname{re}{\left(c\right)}} \right)}}{2} + \frac{e^{2 \left(- \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)}\right) e^{\operatorname{re}{\left(c\right)}}} \cos{\left(2 \left(\sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) e^{\operatorname{re}{\left(c\right)}} \right)}}{2} - \frac{1}{2}

-1/2 + cos(2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*exp(re(c)))*exp(2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*exp(re(c)))/2 + i*exp(2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*exp(re(c)))*sin(2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*exp(re(c)))/2

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

log(2*x+1)/2=e^c*(y+1) la ecuación

Solución numérica:

Solución

log(2x+1)/2=e^c(y+1) la ecuación