Question

If ${\log }_{10}m+{\log }_{10}n={\log }_{10}(m+n)$ and $m=7$, then the value of $n$ is

• A. $5$
• B. $\frac{2}{3}$
• C. $\frac{7}{6}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{7}{6}$

Given:-

${\log }_{10}m+{\log }_{10}n=lo{g}_{10}(m+n)$

and $m=7$

To find:- $n$

Sol:-

${\log }_{10}m+{\log }_{10}n={\log }_{10}(m+n)$

${\log }_{10}\left(mn\right)={\log }_{10}(m+n)$

$\Rightarrow m.n=m+n$

as $m=7$

$7n=7+n$ $\Rightarrow 7n-n=7$

$6n=7$ $\Rightarrow n=\frac{7}{6}$

Hence the correct answer is $\frac{7}{6}$