Logarithms-25

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Evaluate :

(i) (6.32) 3 X (83.94) 1 / 4

(ii) [(17.42) 2 / 3 X 18.42] / (126.37) 1 / 2

Solution:

(i) Let x = (6.32) 3 X (83.94) 1 / 4

=> log x = 3 log 6.32 + (1 / 4) log 83.94

= 3 X 0.8007 + (1 / 4) X 1.9240

= 2.4021 + 0.4810

= 2.8831

=> x = antilog 2.8831 = 764.0

(ii) Let x = [(17.42) 2 / 3 X 18.42] / (126.37) 1 / 2

Therefore, log x = (2 / 3) log 17.42 + log 18.42 - (1 / 2) log 126.4

= (2 / 3) (1.2410) + 1.2653 - (1 / 2) (2.1018)

= 0.8273 + 1.2653 - 1.0509 = 1.0417

Therefore, x = antilog 1.0417 = 11.01

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