Question

Sum of all solution (s) of the equation ${\log }_{10}\left(x\right)+{\log }_{10}(x+2)-{\log }_{10}(5x+4)=0$ is

• A. -1
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B 3

${\log }_{10}\left(x\right)+{\log }_{10}(x+2)-{\log }_{10}(5x+4)=0$

$\Rightarrow {\log }_{10}\left[\frac{x(x+2)}{5x+4}\right]=0$

$\Rightarrow (x^2+2x)=(5x+4)$

$\Rightarrow x^2-3x-4=0$

$\Rightarrow (x-4)(x+1)=0$

$\Rightarrow x=-1,4$

Sum of solutions of $x=-1+4=3$