Question

Simplify: 2 log 3 -1/2 log 16 +log 12
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Answer 1

Answer:

log27 is the correct answer.

Answer 2

2 log 3 -1/2 log 16 +log 12

= log 3 ² - log √16 + log 12

= log 9 - log 4 + log 12

= log 9 + log 12 - log 4

[∵ we know that in logarithms the (-) is replaced by division and (+) is replaced by multiplication.]

= log (9*12/4)

= log (9*3)

= log 27

= log 3³

= 3 log 3

So, 2 log 3 -1/2 log 16 +log 12 = 3 log 3.