Find the logarithm of 144 to the base two root three?

Answer 1

4

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log (base 2 sqrt 3) of 144 = log 144/log (2 sqrt 3) = log (12^2)/log(2 sqrt 3)
12 = 4*3 --> 12 = (2 sqrt 3)^2 =>
=> log (12^2)/log(2 sqrt 3) = 2 log 12/log (2 sqrt 3) = 4 log (2 sqrt 3)/log(2 sqrt 3) = 4