Powers of products and quotients answers
Asked by maham237 @ in Mathematics viewed by 287 People
Provide an example of the product, quotient, and power properties of logarithm
Answered by maham237 @
Answer:
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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