Log 3^2 ,log6^2 , log 12 ^2 are in
Answers
Answer:
Arithmetic Progression(A.P)
Step-by-step explanation:
We say a, b and c are in Arithmetic Progresson(A.P),
if b-a = c-b
We will be using some properties of logarithms here,
log aⁿ = n log a-------(*) and
log b - log a = log (b/a)-------(**).
Consider log6² - log3² = log(6²/3²)=
log2²(using log b - log a = log (b/a)))
= 2 log 2, (using log aⁿ = n log a),
and log12² - log6² = log(12²/6²)
=log2², using log b - log a = log (b/a).
=2log2 using log aⁿ = n log a.
Since ,both have the same common difference, we say that the given numbers are in A.P
Answer:
Step-by-step explanation:
log(3²), log(6²), log(12²) are in A.P
Concept:
1. Quotient rule:
log(M/N) = logM - logM
2. If b - a = c - b then a, b, c are in AP
log(3²)= log 9
log(6²)= log 36
log(12²)= log 144
log 36 - log 9 = log(36/9) = log 4
log 144 - log 36 = log(144/36) = log 4
log 36 - log 9 =log 144 - log 36
⇒ log9, log36, log144 are in A.P
Hence log(3²), log(6²), log(12²) are in A.P