Question

Solve the following equation:
$\log 5+\log (x+10)-1=\log (21x-20)-\log (2x-1)$

Answer 1

$log5+log(x+10)-1=log(21x-20)-log(2x-1)\Rightarrow log\left[\frac{5(x+10)}{10}\right]=log\left(\frac{21x-20}{2x-1}\right)\Rightarrow \frac{x+10}{2}=\frac{21x-20}{2x-1}\Rightarrow (2x-1)(x+10)=42x-40\Rightarrow {2x}^2+19x-10=42x-40\Rightarrow {2x}^2-23x+30=0\Rightarrow {2x}^2-20x-3x+30=0\Rightarrow (2x-3)(x-10)\Rightarrow x=\frac{3}{2}$

or $x=10.$