Solve this equation 4^(log_2(x))-2^(log_2(x))=3^(log_3(12))

spatularificw2

spatularificw2

Answered question

2022-09-09

Solve this equation 4 log 2 ( x ) 2 log 2 ( x ) = 3 log 3 ( 12 )
I thought to write 2 log 2 ( x ) 2 2 log 2 ( x ) = 3 log 3 ( 12 ) . Then is there a way to factorize 2 log 2 ( x ) ? I don't know how to proceed...

Answer & Explanation

Helena Bentley

Helena Bentley

Beginner2022-09-10Added 10 answers

Let log 2 x = t, then 2 log 2 ( x ) = 2 t = x. Thus the given equation is
x 2 2 x = 12
Genesis Gibbs

Genesis Gibbs

Beginner2022-09-11Added 2 answers

Hint:
We have a log a ( b ) = b and we have the following:
4 log 2 ( x ) = 2 2 log 2 ( x ) = ( 2 log 2 ( x ) ) 2 = x 2

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