How can 1/2 log(x) = log(sqrt(x))?

cvnoticiasdg

cvnoticiasdg

Open question

2022-08-20

How can 1 2 log ( x ) = log ( x )?
How can log ( x ) 2 = log ( x ) ?
How would I come to this conclusion?

Answer & Explanation

ESCOMESWISKvh

ESCOMESWISKvh

Beginner2022-08-21Added 6 answers

I assume that you know log ( a b ) = log a + log b. Then
log x = log ( x x ) = log x + log x = 2 log x
and so
log x = 1 2 log x .
Anyway, it's just a special case of the general law
log ( x k ) = k log x
(for x > 0 and any k).
Braeden Valenzuela

Braeden Valenzuela

Beginner2022-08-22Added 3 answers

You know the rules?
A log ( x ) = log ( x A )
With A = 1 2 , we obtain what you are asking for.

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