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

1) Product property

2) quotient property

3) Power property

Step-by-step 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]