Question

If $\log (m+n)=\log m+\log n$, then:

• A. $mn=1$
• B. $m=-n$
• C. $\frac{m}{(m-1)}=n$
• D. $\frac{m}{n}=1$

Answer 1

The correct option is C $\frac{m}{(m-1)}=n$

if $\log m+\log n=\log (m+n),$ find $m$ in terms of $n$

We can write this as: $\log \left(mn\right)=\log (m+n)$

$\therefore mn=m+n$

Subtracting n from both the sides we get,

$mn–n=m$

$n(m-1)=m$

$\frac{m}{m-1}=n$