Question

Solve: ln(x – 3) = ln(7x – 23) –  ln(x + 1)

Answer 1

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