Question

if log (x+1) - log(x-2) =log 3 then find x
​

Answer 1

Solution:-

$\begin{gathered}\\\implies\quad \sf log (x+1) - log(x-2) =log 3 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf log(\frac{x+1}{x-2})= log \:3 \\\end{gathered}\quad(log\:a-log\:b = log (\frac{a}{b}))$

Taking antilogs both sides -

$\begin{gathered}\\\implies\quad \sf \frac{(x+1)}{(x-2)}=3 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf x+1 = 3(x-2) \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf x+1 = 3x-6 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf x-3x= -6-1 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf -2x = -7 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf x = \frac{-7}{-2} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \boxed{\sf {x = \frac{7}{2}}} \\\end{gathered}$