Question

log3(4x-5)-log3(x+1)=0

Answer 1

Log3(4x-5)-log3(x+1)=0

Resolvemos:

$Log3(4x-5)-log3(x+1)=0 \\ \\ \log _{10}\left(3\right)\cdot 4x-\log _{10}\left(3\right)\cdot \:5-\log _{10}\left(3\right)x-\log _{10}\left(3\right) =0 \\ \\ \textbf{Simplificamos:} \\ \\ 4\log _{10}\left(3\right)x-5\log _{10}\left(3\right)-\log _{10}\left(3\right)x-\log _{10}\left(3\right)=0 \\ \\ 4\log _{10}\left(3\right)x-6\log _{10}\left(3\right)-\log _{10}\left(3\right)x=0$

$3\log _{10}\left(3\right)x-6\log _{10}\left(3\right)=0 \\ \\ 3\log _{10}\left(3\right)x-6\log _{10}\left(3\right)+6\log _{10}\left(3\right)=0+6\log _{10}\left(3\right) \\ \\ 3\log _{10}\left(3\right)x=6\log _{10}\left(3\right) \\ \\ \dfrac{3\log _{10}\left(3\right)x}{3\log _{10}\left(3\right)}=\dfrac{6\log _{10}\left(3\right)}{3\log _{10}\left(3\right)} \\ \\ \boxed{\boxed{x=2}} \ \ Respuesta$

¡Espero haberte ayudado, saludos... G.G.H!