Find x =log_2(4^(3/4)*sqrt(2^5))^(1/2) I am looking for x. x =log_2 [(4^(3/4)*sqrt(2^5))^(1/2)] I am not sure how to do this.

Amiya Melendez

Amiya Melendez

Answered question

2022-10-26

Find x = log 2 ( 4 3 4 2 5 ) 1 2
I am looking for x.
x = log 2 [ ( 4 3 4 2 5 ) 1 2 ]
I am not sure how to do this.
I am trying to solve this by changing the form like this:
x = log a b a x = b
thanks.

Answer & Explanation

DoryErrofbi

DoryErrofbi

Beginner2022-10-27Added 12 answers

x = log 2 ( 4 3 4 2 5 ) 1 2 = 1 2 log 2 ( 2 3 / 2 × 2 5 / 2 ) = 1 2 log 2 2 4 = 4 2 log 2 2 = 2   .
gasavasiv

gasavasiv

Beginner2022-10-28Added 3 answers

Use sum rule to get x = 1 / 2 ( l o g 2 ( 4 3 / 4 .2 5 / 2 ) )
= 1 / 2 ( l o g 2 ( 4 3 / 4 ) + l o g 2 ( 2 5 / 2 ) )
= 1 / 2 ( 3 / 4 ( l o g 2 ( 4 ) ) + 5 / 2 ( l o g 2 ( 2 ) ) )
= 1 / 2 ( 3 / 4 ( l o g 2 ( 2 2 ) ) + 5 / 2 ( l o g 2 ( 2 ) ) )
= 1 / 2 ( 3 / 4 ( 2 l o g 2 ( 2 ) ) + 5 / 2 ( l o g 2 ( 2 ) ) )
= 1 / 2 ( 3 / 2 ( l o g 2 ( 2 ) ) + 5 / 2 ( l o g 2 ( 2 ) ) )
= 2 ( l o g 2 ( 2 ) )

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