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lncx=-ln(t(e^(2/sqrt(t)))) la ecuación

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Solución

Ha introducido [src] 
               /     2  \
               |   -----|
               |     ___|
               |   \/ t |
log(c*x) = -log\t*E     /
log⁡(cx)=−log⁡(e2tt)\log{\left(c x \right)} = - \log{\left(e^{\frac{2}{\sqrt{t}}} t \right)}
Simplificar
Solución detallada
Tenemos la ecuación
log⁡(cx)=−log⁡(e2tt)\log{\left(c x \right)} = - \log{\left(e^{\frac{2}{\sqrt{t}}} t \right)}
log⁡(cx)=−log⁡(te2t)\log{\left(c x \right)} = - \log{\left(t e^{\frac{2}{\sqrt{t}}} \right)}
Es la ecuación de la forma:
log(v)=p

Por definición log
v=e^p

entonces
cx=e(−1)log⁡(te2t)1c x = e^{\frac{\left(-1\right) \log{\left(t e^{\frac{2}{\sqrt{t}}} \right)}}{1}}
simplificamos
cx=e−2ttc x = \frac{e^{- \frac{2}{\sqrt{t}}}}{t}
x=e−2tctx = \frac{e^{- \frac{2}{\sqrt{t}}}}{c t}
Gráfica
Suma y producto de raíces [src] 
suma
    /  -2  \     /  -2  \
    | -----|     | -----|
    |   ___|     |   ___|
    | \/ t |     | \/ t |
    |e     |     |e     |
I*im|------| + re|------|
    \ c*t  /     \ c*t  /
re⁡(e−2tct)+iim⁡(e−2tct)\operatorname{re}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} + i \operatorname{im}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} 
=
    /  -2  \     /  -2  \
    | -----|     | -----|
    |   ___|     |   ___|
    | \/ t |     | \/ t |
    |e     |     |e     |
I*im|------| + re|------|
    \ c*t  /     \ c*t  /
re⁡(e−2tct)+iim⁡(e−2tct)\operatorname{re}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} + i \operatorname{im}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} 
producto
    /  -2  \     /  -2  \
    | -----|     | -----|
    |   ___|     |   ___|
    | \/ t |     | \/ t |
    |e     |     |e     |
I*im|------| + re|------|
    \ c*t  /     \ c*t  /
re⁡(e−2tct)+iim⁡(e−2tct)\operatorname{re}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} + i \operatorname{im}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} 
=
    /  -2  \     /  -2  \
    | -----|     | -----|
    |   ___|     |   ___|
    | \/ t |     | \/ t |
    |e     |     |e     |
I*im|------| + re|------|
    \ c*t  /     \ c*t  /
re⁡(e−2tct)+iim⁡(e−2tct)\operatorname{re}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} + i \operatorname{im}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} 
i*im(exp(-2/sqrt(t))/(c*t)) + re(exp(-2/sqrt(t))/(c*t))
Respuesta rápida [src] 
         /  -2  \     /  -2  \
         | -----|     | -----|
         |   ___|     |   ___|
         | \/ t |     | \/ t |
         |e     |     |e     |
x1 = I*im|------| + re|------|
         \ c*t  /     \ c*t  /
x1=re⁡(e−2tct)+iim⁡(e−2tct)x_{1} = \operatorname{re}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} + i \operatorname{im}{\left(\frac{e^{- \frac{2}{\sqrt{t}}}}{c t}\right)} 
x1 = re(exp(-2/sqrt(t))/(c*t)) + i*im(exp(-2/sqrt(t))/(c*t))
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