How does (log sqrt x)^2=1/4(log x)^2? To be specific, why the removal of root, and how do we get 4 in denominator?

ter3k4w8x

ter3k4w8x

Answered question

2022-10-08

How does ( log x ) 2 = 1 4 ( log x ) 2 ?
To be specific, why the removal of root, and how do we get 4 in denominator?

Answer & Explanation

Maddox Koch

Maddox Koch

Beginner2022-10-09Added 7 answers

Recall:
log ( a b ) = b log a
Here, that means that
log ( x ) = log x 1 / 2 = 1 2 log x
So
( log x ) 2 = ( log x 2 ) 2 = ( log x ) 2 2 2 ( a b ) c = a c b c = 1 4 ( log x ) 2

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