Question

log(4,5-x) = log 4,5 - log x​

Answer 1

Respuesta:       $\quad x=1.5,\:x=3\right)$

Pasos:

$log\left(4.5-x\right)\:=\:log\:4.5\:-\:log x$

$\log _{10}\left(4.5-x\right)=\log _{10}\left(4.5\right)-\log _{10}\left(x\right)$

$\mathrm{Sumar\:}\log _{10}\left(x\right)\mathrm{\:a\:ambos\:lados}$

$\log _{10}\left(4.5-x\right)+\log _{10}\left(x\right)=\log _{10}\left(4.5\right)-\log _{10}\left(x\right)+\log _{10}\left(x\right)$

$\mathrm{Simplificar}$

$\log _{10}\left(4.5-x\right)+\log _{10}\left(x\right)=\log _{10}\left(4.5\right)$

$\mathrm{Aplicar\:las\:propiedades\:de\:los\:logaritmos}:\quad \log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)$

$\log _{10}\left(4.5-x\right)+\log _{10}\left(x\right)=\log _{10}\left(\left(4.5-x\right)x\right)$

$\log _{10}\left(\left(4.5-x\right)x\right)=\log _{10}\left(4.5\right)$

$\left(4.5-x\right)x=4.5$

$x=\frac{4.5-\sqrt{2.25}}{2},\:x=\frac{4.5+\sqrt{2.25}}{2}$

$\left(\mathrm{Decimal}:\quad x=1.5,\:x=3\right)$