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Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})?
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Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})?
Calculation of Logarithm Expression
- First, calculate the logarithm of 27 to the base 3:
log₃(27) = 3, as 3 raised to the power of 3 gives 27.
- Then, substitute this value into the expression:
log₂(log₂(log₃(27)³))
= log₂(log₂(3³))
= log₂(log₂(27))
= log₂(4.7549) [approximately]
Conversion to Log base 10
- To convert log base 2 to log base 10, we use the change of base formula:
log₂(x) = log₁₀(x) / log₁₀(2)
- Applying this formula to the result obtained:
log₂(4.7549) ≈ log₁₀(4.7549) / log₁₀(2)
- Further simplifying:
≈ 0.677 / 0.301
≈ 2.249 [approximately]
Final Calculation
- Finally, we convert the log base 10 back to log base 2:
log₂(2.249) ≈ log₁₀(2.249) / log₁₀(2)
- Calculating this:
≈ 0.351 / 0.301
≈ 1.167 [approximately]
Therefore, log to the base 2 of {log base 2 (log base 3 (27)³)} is approximately 1.167.
- First, calculate the logarithm of 27 to the base 3:
log₃(27) = 3, as 3 raised to the power of 3 gives 27.
- Then, substitute this value into the expression:
log₂(log₂(log₃(27)³))
= log₂(log₂(3³))
= log₂(log₂(27))
= log₂(4.7549) [approximately]
Conversion to Log base 10
- To convert log base 2 to log base 10, we use the change of base formula:
log₂(x) = log₁₀(x) / log₁₀(2)
- Applying this formula to the result obtained:
log₂(4.7549) ≈ log₁₀(4.7549) / log₁₀(2)
- Further simplifying:
≈ 0.677 / 0.301
≈ 2.249 [approximately]
Final Calculation
- Finally, we convert the log base 10 back to log base 2:
log₂(2.249) ≈ log₁₀(2.249) / log₁₀(2)
- Calculating this:
≈ 0.351 / 0.301
≈ 1.167 [approximately]
Therefore, log to the base 2 of {log base 2 (log base 3 (27)³)} is approximately 1.167.
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Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})?
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Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})?.
Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Log to the base 2 ( log base 2 {log base 2(log base 3 (27)³})?.
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