Question

Solve: ln(x – 3) = ln(7x –  23) 

–  ln(x  + 1)

Answer 1

`Formula\ for\ lagarythm:\\ log_ab=c\ \ \ ----> a^c=b\\\\Base\ of\ ln \ is\ e=2,7\\\\ln(x-3)=ln(7x-23)-ln(x+1)\\\\ ln(x-3)=ln((7x-23)/(x+1))\ \ \ | subtract\ ln((7x-23)/(x+1))\\\\ ln(((7x-23)/(x+1))/(x-3))=0\\\\ ln((7x-23)/((x+1)(x-3)))=0\\\\ 2,7^0=(7x-23)/((x+1)(x-3))\\\\ 1=(7x-23)/((x+1)(x-3))\ \ \ | multiply\ by\ (x+1)(x-3)\\\\ (x+1)(x-3)=7x-23\\\\ x^2-3x+x-3=7x-23\\\\ x^2-9x-26=0\\\\x=(1)/(2)(9-√(185))\ \ or\ \ x=(1)/(2)(9+√(185))`