If ${\log }_{10}5+{\log }_{10}(5x+1)={\log }_{10}(x+5)+1$, then $x$ is equal to

The correct option is B: 3
We have, ${\log }_{10}5+{\log }_{10}(5x+1)={\log }_{10}(x+5)+1$

$\Rightarrow {\log }_{10}5+{\log }_{10}(5x+1)={\log }_{10}(x+5)+{\log }_{10}10[{\log }_{10}10=1]$

$\Rightarrow {\log }_{10}\left[5\right(5+1\left)\right]={\log }_{10}\left[10\right(x+5\left)\right]\left\{\right(\log a+\log b=\log (a\times b)\}$

$\Rightarrow 5(5x+1)=10(x+5)$

$\Rightarrow 5x+1=2(x+5)$

$\Rightarrow 5x+1=2x+10$

$\Rightarrow 3x=9$

$\therefore x=3$