What is the domain of this function? (Don't know how to solve it, logarithms...) Please explain how

Anthony Kramer

Anthony Kramer

Answered question

2022-05-28

What is the domain of this function? (Don't know how to solve it, logarithms...)
Please explain how you solved it, thanks.
f ( x ) = log x 2 log 2 x

Answer & Explanation

tatoas9f

tatoas9f

Beginner2022-05-29Added 11 answers

First x should be positive and x 1. Moreoer
log x 2 log 2 x = log 2 log x log x log 2 = log 2 2 log 2 x log 2 log x = ( log 2 log x ) ( log 2 + log x ) log 2 log x 0 x [ 0 , 1 2 ) ( 1 , 2 ]
so the domain of definition is [ 0 , 1 2 ) ( 1 , 2 ]
Brice Colon

Brice Colon

Beginner2022-05-30Added 3 answers

Hint
Going, from definition, to natural logarithms, you have
f ( x ) = log x 2 log 2 x = log ( 2 ) log ( x ) log ( x ) log ( 2 )
I am sure you can take from here.

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