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Logaritmo log
log(5)*sqrt(x-1)^2-10=6*log(5)*(|x-1|)
log(y)=-x^2/4
log(t)+k*t-log(b)-k*b=k*m*a*c
log3(x-2)+log3x=log38
log2cos(x)=0.2

(-log(u-1)-4)/(u-1)=c+log(x-1) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

-log(u - 1) - 4                 
--------------- = c + log(x - 1)
     u - 1

\frac{- \log{\left(u - 1 \right)} - 4}{u - 1} = c + \log{\left(x - 1 \right)}

Simplificar

Solución detallada

Tenemos la ecuación

\frac{- \log{\left(u - 1 \right)} - 4}{u - 1} = c + \log{\left(x - 1 \right)}

Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo

- \log{\left(x - 1 \right)} = c + \frac{\log{\left(u - 1 \right)} + 4}{u - 1}

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

\log{\left(x - 1 \right)} = - c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}

Es la ecuación de la forma:

log(v)=p

Por definición log

v=e^p

entonces

x - 1 = e^{\frac{c + \frac{\log{\left(u - 1 \right)} + 4}{u - 1}}{-1}}

simplificamos

x - 1 = e^{- c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}}

x = e^{- c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}} + 1

Gráfica

Respuesta rápida [src]

                                                                                                                                                                                                                                                                                                                                                           4                         log(|-1 + u|)                      re(c*u)                          re(c)                          4*re(u)                       im(c)*im(u)                     re(c)*re(u)                  arg(-1 + u)*im(u)                 im(u)*im(c*u)                log(|-1 + u|)*re(u)                re(u)*re(c*u)                            4                         log(|-1 + u|)                      re(c*u)                          re(c)                          4*re(u)                       im(c)*im(u)                     re(c)*re(u)                  arg(-1 + u)*im(u)                 im(u)*im(c*u)                log(|-1 + u|)*re(u)                re(u)*re(c*u)                                                                                                                                                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                             ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------      ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                   2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                         2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                                                                                                                                                                                                                                                                                                                                                
            /         arg(-1 + u)                       im(c*u)                          im(c)                          4*im(u)                       im(c)*re(u)                 im(u)*log(|-1 + u|)                im(u)*re(c*u)                 arg(-1 + u)*re(u)                  im(u)*re(c)                    im(c*u)*re(u)        \  1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)      1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)    /         arg(-1 + u)                       im(c*u)                          im(c)                          4*im(u)                       im(c)*re(u)                 im(u)*log(|-1 + u|)                im(u)*re(c*u)                 arg(-1 + u)*re(u)                  im(u)*re(c)                    im(c*u)*re(u)        \
x1 = 1 + cos|----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------|*e                                                                                                                                                                                                                                                                                                                                                              + I*e                                                                                                                                                                                                                                                                                                                                                             *sin|----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------|
            |      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2                      2        2             |
            \1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)/                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)   1 + im (u) + re (u) - 2*re(u)/

x_{1} = i e^{- \frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\log{\left(\left|{u - 1}\right| \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c\right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{4 \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1}} \sin{\left(\frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4 \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} \right)} + e^{- \frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\log{\left(\left|{u - 1}\right| \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c\right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{4 \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1}} \cos{\left(\frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4 \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} \right)} + 1

x1 = i*exp(-log(|u - 1|)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + log(|u - 1|)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - 4*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4/(re(u)^2 - 2*re(u) + im(u)^2 + 1))*sin(log(|u - 1|)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(u)*im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1)) + exp(-log(|u - 1|)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + log(|u - 1|)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - 4*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4/(re(u)^2 - 2*re(u) + im(u)^2 + 1))*cos(log(|u - 1|)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(u)*im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1)) + 1

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¿Cómo usar?

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(-log(u-1)-4)/(u-1)=c+log(x-1) la ecuación

Solución numérica:

Solución