Find the value of log₂ ( log₂ . log₃81 ) ....
Answers
Answered by
10
Required Answer:-
Given to Evaluate:
- log₂ [log₂(log₃81)]
Solution:
We have,
log₂[log₂(log₃81)]
= log₂[log₂(log₃ 3⁴)] [As 3⁴ = 81]
= log₂[log₂(4 × log₃(3))] [As log(x)ⁿ = n log(x)]
= log₂[log₂(4)] [3¹ = 1 So, log₃(3) = 1]
= log₂[log₂(2²)] [As 2² = 4]
= log₂[2 × log₂(2)] [As log(x)ⁿ = n log(x)]
= log₂[2] [On simplifying]
= 1 [2¹ = 2 So log₂(2) = 1]
Hence, the required answer is 1.
Answer:
- On simplifying, we get the result 1.
Answered by
9
Given to Evaluate:
log₂ [log₂(log₃81)]
Solution:
We have,
log₂[log₂(log₃81)]
= log₂[log₂(log₃ 3⁴)] [As 3⁴ = 81]
= log₂[log₂(4 × log₃(3))] [As log(x)ⁿ = n log(x)]
= log₂[log₂(4)] [3¹ = 1 So, log₃(3) = 1]
= log₂[log₂(2²)] [As 2² = 4]
= log₂[2 × log₂(2)] [As log(x)ⁿ = n log(x)]
= log₂[2] [On simplifying]
= 1 [2¹ = 2 So log₂(2) = 1]
Hence, the required answer is 1.
Answer:
On simplifying, we get the result 1.
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