Question

if log(m+n)= log m+ log n;prove: n=m/(m-1)

Answer 1

log(m+n)= logm+ logn

log(m+n) = log(mn). [ loga+logb =log ab]

log on both sides geys cancel
then,

m+n = mn => m= mn -n
=> m = n(m-1)
=> n = m/m-1 [proved]

Answer 2

It is proces that $n=\frac{m}{(m-1)}$

Step-by-step explanation:

Given:

$\rightarrow \: log(m + n) = log(m) + log(n) \\ \rightarrow \: log(m + n) = \: log(m n) \\ \rightarrow \: (m + n) =mn \\ \rightarrow \: m =mn - n \\ \rightarrow \: m = n(m - 1) \\ \rightarrow \: n = \frac{m}{(m - 1)}$

Hence proved.