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]

i'm assuming it's looking for the missing length, which should be 4cm

hope this !