Question

Evaluate the following using log tables.

(27.8)^1/2 x (58.49)^2/3
/(0.0007)^1/4​

Answer 1

Given : (27.8)^1/2 x (58.49)^2/3  /(0.0007)^1/4​  

To Find : Evaluate the following using log tables

Solution:

(27.8)^1/2 x (58.49)^2/3  /(0.0007)^1/4​

Let say N  = (27.8)^1/2 x (58.49)^2/3  /(0.0007)^1/4​

Taking log both sides

=> log  N = log { (27.8)^1/2 x (58.49)^2/3  /(0.0007)^1/4​ }

log (ab/c) = log a + log b - log c

=>  log  N = log   (27.8)^1/2 + log (58.49)^2/3  - log (0.0007)^1/4​  

log aⁿ = n log a

=> log  N = (1/2) log (27.8) + (2/3) log(58.49) - (1/4) log (0.0007)

=> log  N = (1/2) log (278/10) + (2/3) log(5849/100) - (1/4) log (7/10000)

=>  log  N = (1/2) (log278 - log 10) + (2/3) (log5849 - log 100) - (1/4) (log 7 - log 10000)

=>  log  N = (1/2) (log278 - 1) + (2/3) (log5849 - 2) - (1/4) (log 7 - 4)

=> log  N = (1/2) (2.444 - 1) + (2/3) (3.767 - 2) - (1/4) (0.845 - 4)

=> log  N = (1/2) (1.444) + (2/3) (1.767) - (1/4) (-3.155)

=>  log  N =0.722 + 1.178 + 0.78875

=>  log  N = 2.68875

=> N = 488.4

(27.8)^1/2 x (58.49)^2/3  /(0.0007)^1/4​   =  488.4

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