Question

Solve the following equations.
${\log }_5\left(\frac{2+x}{10}\right)={\log }_5\left(\frac{2}{x+1}\right)$

Answer 1

${\log }_5\left(\frac{2+x}{10}\right)-{\log }_5\left(\frac{2}{x+1}\right)=0\frac{(2+x)(x+1)}{10\times 2}=1x^2+3x+2=20x^2+3x-18=0(x-3)(x+6)=0x=3,-6$