Question

(57.8)^1/2 × (0.0027)^1/3​
Evaluate using Log Tables​

Answer 1

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

Answer 2

Hdieyx
Gyjeeh
Shendhdjs
Djdudnd
S
Dndjdk