Question

Please answer me no. 12 part 1

Answer 1

$log(m + n) = log(m ) + log(n) \\ log(m + n) = log(mn) \\ taking \: antilog \: both \: sides \\ \\ m + n = mn \\ m - mn = - n \\ m(1 - n) = - n \\ m = \frac{ - n}{1 - n} \\ m = \frac{n}{n - 1}$
hope this will help you.

Answer 2

We know, log(a) + log(b) = log(ab) (formula)

Using the formula, we get

log(m) + log(n) = log(mn)

Thus, log(m + n) = log(mn)

which implies that "m + n = mn"

so,

→m + n = mn

→n = mn - m

→n = m(n - 1)

→ n/(n - 1) = m

Hence proved

Hope it helps!!