Question

Log x - Log y = 1
Log x + Log y = 3​

Answer 1

Respuesta:  $\begin{pmatrix}x=100,\:&y=10\end{pmatrix}$

Explicación paso a paso:

$\log _{10}\left(x\right)-\log _{10}\left(y\right)=1,\:\log _{10}\left(x\right)+\log _{10}\left(y\right)=3\quad$

$\mathrm{Sumar\:las\:ecuaciones}$

$\log _{10}\left(x\right)-\log _{10}\left(y\right)=1$

$+$

$\underline{\log _{10}\left(x\right)+\log _{10}\left(y\right)=3}$

$\log _{10}\left(x\right)-\log _{10}\left(y\right)+\left(\log _{10}\left(x\right)+\log _{10}\left(y\right)\right)=1+3$

$\mathrm{Simplificar}$

$2\log _{10}\left(x\right)=4$

$\mathrm{Resolver\:}\:2\log _{10}\left(x\right)=4:\quad x=100$

$\mathrm{Sustituir\:las\:soluciones\:}x=100\mathrm{\:en\:}\log _{10}\left(x\right)-\log _{10}\left(y\right)=1$

$\mathrm{Para\:}\log _{10}\left(x\right)-\log _{10}\left(y\right)=1\mathrm{,\:sustituir\:}x\mathrm{\:con\:}100:\quad y=10$

$\mathrm{Por\:lo\:tanto,\:la\:solucion\:final\:para\:}\log _{10}\left(x\right)-\log _{10}\left(y\right)=1,\:\log _{10}\left(x\right)+\log _{10}\left(y\right)=3\mathrm{\:es\:}$

$\begin{pmatrix}x=100,\:&y=10\end{pmatrix}$