Question

if log ( m + n) = log m + log n , show that n = m/ m -1

Answer 1

$\underline{\mathfrak{ Solution : \:}}$

$\mathsf{ \implies log \: (m \: + \: n ) \: = \: log \: m \: + \: log \: n} \\ \\ \textsf{ Using \: identity : } \\ \\ \boxed{\mathsf{ \implies log \: a \: + \: log \: b \: = \: log \: ( ab )}} \\ \\ \mathsf{ \implies log \: (m \: + \: n) \: = \: log \: (mn)}$

$\textsf{ Using \: antilog : } \\ \\ \mathsf{ \implies m \: + \: n \: = \: mn} \\ \\ \mathsf{ \implies m \: = \: mn \: - \: n} \\ \\ \mathsf{ \implies m \: = \: n( m \: - \: 1)} \\ \\ \mathsf{ \implies n \: = \: \dfrac{m}{(m \: - \: 1)} }$

$\boxed{\underline{\mathfrak{ Proved !! }}}$