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16 October, 19:37

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

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  1. 16 October, 22:16
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    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]
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