Prove that log4(3) = log2(3)^1/2

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log4(3) = log2(3)^1/2

Guest Jan 19, 2015

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Best Answer

log₄3 = x ---> 4^x = 3 ---> (2²)^x = 3 ---> 2^2x = 3 ---> √(2^2x) = √3

---> (2^2x)^1/2 = (3)^1/2 ---> 2^x = (3)^1/2 ---> log₂(3)^1/2 = x

Therefore, log₄3 = log₂(3)^1/2

geno3141 Jan 19, 2015

geno3141 · Answer 1 · 2015-01-19T06:18:39

log₄3 = x ---> 4^x = 3 ---> (2²)^x = 3 ---> 2^2x = 3 ---> √(2^2x) = √3

---> (2^2x)^1/2 = (3)^1/2 ---> 2^x = (3)^1/2 ---> log₂(3)^1/2 = x

Therefore, log₄3 = log₂(3)^1/2