Prove laws of logarithm?

log_c (ab) = log_c a + log_c b

Proof: Let log_c (ab) = d,  log_c a = e,  log_c b = f;

Hence, we can write, d = e + f            ... (1)

c^d = ab and c^e = a, c^f = b              .. using logarithm definition,

 

Now ab = axb

c^d = c^e x c^f

 

c^d = c^e+f

Which gives, d = e + f.

Similarly we can prove other laws.

Regards,

Team,

TopperLearning.