Question

lf ${\log }_{10}m+{\log }_{10}n={\log }_{10}(m+n)$ 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 $\frac{7}{6}$

Apply the relation $\log a+\log b=\log ab$ and if $\log x=\log y$, then $x=y$.

Given, that $m=7$ and ${\log }_{10}m+{\log }_{10}n={\log }_{10}(m+n)$

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

$\Rightarrow mn=m+n$

Substituting $m=7$, we get

$7n=7+n$

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