Question

Derive the product law of logarithms

Answer 1

Answer:

㏒abₓ = ㏒aₓ +㏒bₓ

Step-by-step explanation:

let ㏒abₓ = p

⇒ x^p=ab    ...(1)

㏒aₓ=q

⇒x^q=a ....(2)

㏒bₓ=r

⇒x^r=b ....(3)

multiply (2) & (3)

x^q * x^r = ab

x^a+r=x^p (from (1))

q+r=p

㏒aₓ +㏒bₓ = ㏒abₓ