The simplified form of log (75/16) – 2 log (5/9) + log (32/343) is ?

A . log 2

B . 2 log 2

C . log 3

D . log 5

Answer : A . log 2

Explanation:

Given:
= log75/16 – 2 log5/9 + log32/343
= log [(25 x 3)/(4 x 4)] – log (25/81) + log [(16 x 2)/(81 x 3)] = log(25 x 3) – log ( 4 x 4 ) – log(25) + log81 + log(16 x 2) – log (81 x 3)
= log 25 + log 3 – log 16 – log 25 + log 81 + log 16 + log 2 – log 81 – log 3
= log 2

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Logarithm

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