Question

If ${\log }_{10}m=b-{\log }_{10}n$, then $m=$

• A. $b/n$
• B. $bn$
• C. ${10}^{b}n$
• D. $b-{10}^n$
• E. ${10}^b/n$

Answer 1

The correct option is E ${10}^b/n$

$b={\log }_{10}m+{\log }_{10}n={\log }_{10}mn\therefore mn={10}^b;\therefore m={10}^b/n$; or
${\log }_{10}m={\log }_{10}{10}^b-{\log }_{10}n={\log }_{10}\left({10}^b/n\right),\therefore m={10}^b/n$.