Question

Prove the following:-
1. log m/n = log m - log n

2. log mn = log m + log n

Answer 1

$10^a=m$  and  $10^b=n$

log m = a         and      log n = b    ........................ (i) and (ii)

1) so $\frac{10^a}{10^b}=m/n$
  
⇒ $10^{a-b}=m/n$

⇒ log m/n = a - b

⇒ log m/n = log m - log n       {using 1 and 2}

2)

so $10^a*10^b=mn$

⇒ $10^{a+b}=mn$

⇒ log mn = a + b

⇒log m/n = log m + log n       {using 1 and 2}