Evaluate the following using log tables.
(57.8)^1/2 × (0.0027)^1/3
Answers
Given : (57.8)^1/2 × (0.0027)^1/3
To Find : Evaluate using log tables.
Solution:
N = (57.8)^1/2 × (0.0027)^1/3
Taking log both sides
log N = log ( (57.8)^1/2 × (0.0027)^1/3 )
log (ab) =loga + logb
=> log N = log ((57.8)^1/2) + log ((0.0027)^1/3 )
log aⁿ = nlogA
=> log N = (1/2) log ((57.8)) + (1/3) log ((0.0027) )
57.8 = 578/10 , 0.0027 = 27/10000
=> log N = (1/2) { log 578 - log 10 ) + (1/3)( log27 - log 10000 )
log 10 = 1
=> log N = (1/2) (log 578 - 1 ) + (1/3) ( log3³ - log 10⁴ )
=> log N = (1/2) (log 578 - 1 ) + (1/3) ( 3 log3 - 4log 10 )
=> log N = (1/2) (log 578 - 1 ) +log3 - 4/3
log 578 = 2.762
=> log N = (1/2) (2.762 - 1 ) +0.477 - 4/3
=> log N = (1/2) (1.762) +0.477 - 1.333
=> log N = 0.025
Taking antilog both sides
=> N = 1.059
(57.8)^1/2 × (0.0027)^1/3 = 1.059
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Answer:
Given : (57.8)^1/2 × (0.0027)^1/3
To Find : Evaluate using log tables.
Solution:
N = (57.8)^1/2 × (0.0027)^1/3
Taking log both sides
log N = log ( (57.8)^1/2 × (0.0027)^1/3 )
log (ab) =loga + logb
=> log N = log ((57.8)^1/2) + log ((0.0027)^1/3 )
log aⁿ = nlogA
=> log N = (1/2) log ((57.8)) + (1/3) log ((0.0027) )
57.8 = 578/10 , 0.0027 = 27/10000
=> log N = (1/2) { log 578 - log 10 ) + (1/3)( log27 - log 10000 )
log 10 = 1
=> log N = (1/2) (log 578 - 1 ) + (1/3) ( log3³ - log 10⁴ )
=> log N = (1/2) (log 578 - 1 ) + (1/3) ( 3 log3 - 4log 10 )
=> log N = (1/2) (log 578 - 1 ) +log3 - 4/3
log 578 = 2.762
=> log N = (1/2) (2.762 - 1 ) +0.477 - 4/3
=> log N = (1/2) (1.762) +0.477 - 1.333
=> log N = 0.025
Taking antilog both sides
=> N = 1.059
(57.8)^1/2 × (0.0027)^1/3 = 1.059