Question

Provide an example of the product, quotient, and power properties of logarithm

Answer 1

1) Product property

2) quotient property

3) Power property

Explanation:

1) Product Property:- logₐ(MN) = logₐ(M) + logₐ(N)

Consider the below example:-

log₂(4*8) = log₂(4) + log₂(8)

=log₂(2²) + log₂(2³)

=2*log₂(2) + 3*log₂(2) [log₂2=1]

=2+3

=5

2) Quotient Property:- logₐ(M/N) = logₐ(M) - logₐ(N)

Consider the below example:-

log₃(27/9) = log₃(27) - log₃(9)

=log₃(3³) - log₃(3²)

=3*log₃(3) - 2*log₃(3)

=3 - 2 [log₃3=1]

=1

3) Power Property: - logₐ(Mⁿ) = n*logₐ(M)

Consider the example below:-

log₃(27) = log₃(3³)

=3*log₃(3)

=3 [log₃3 = 1]