`log_(2)log_(2)log_(5) 125 `= _______A. 4B. 8C. 0.664D. 1

1.	`log_(2)log_(2)log_(5) 125 `= _______A. 4B. 8C. 0.664D. 1
Answer» Answer is (C) 0.664 log₂ log₂ log₅ 125 = log₂ log₂ log₅ 5³ = log₂ log₂ 3 log₅ 5 (∵ log_b aⁿ = n log_b a) = log₂ log₂ 3 (∵ log₅ 5 = 1) = log₂ (log 3/log 2) (∵ log_a b = log b/log a) = \(\frac{log(\frac{log\,3}{log\,2})}{log\,2}\) \(\simeq\) 0.66444870....... Correct Answer - C Apply laws of logarithm.

Answer»

Answer is (C) 0.664

log₂ log₂ log₅ 125

= log₂ log₂ log₅ 5³

= log₂ log₂ 3 log₅ 5 (∵ log_b aⁿ = n log_b a)

= log₂ log₂ 3 (∵ log₅ 5 = 1)

= log₂ (log 3/log 2) (∵ log_a b = log b/log a)

= \(\frac{log(\frac{log\,3}{log\,2})}{log\,2}\)

\(\simeq\) 0.66444870.......

Correct Answer - C
Apply laws of logarithm.

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