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xy=40; x^lgy=4

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Solución

Ha introducido [src]
x*y = 40
$$x y = 40$$
 log(y)    
x       = 4
$$x^{\log{\left(y \right)}} = 4$$
x^log(y) = 4
Respuesta rápida
$$x_{1} = \frac{2 \sqrt{10}}{e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}}$$
=
$$\frac{2 \sqrt{10}}{e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}}$$
=
1.52913018263282

$$y_{1} = 2 \sqrt{10} e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}$$
=
$$2 \sqrt{10} e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}$$
=
26.1586622606120
$$x_{2} = 2 \sqrt{10} e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}$$
=
$$2 \sqrt{10} e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}$$
=
26.1586622606120

$$y_{2} = \frac{2 \sqrt{10}}{e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}}$$
=
$$\frac{2 \sqrt{10}}{e^{\frac{\sqrt{- \log{\left(256 \right)} + \log{\left(40 \right)}^{2}}}{2}}}$$
=
1.52913018263282