Interval of the solutions to log_(1/2) log_2((1+2x)/(1+x))>0 is?

Jaelyn Payne

Jaelyn Payne

Answered question

2022-10-15

Interval of the solutions to log 1 / 2 log 2 ( 1 + 2 x 1 + x ) > 0 is?
I consistently get x>−1 but that doesn't fit the possible solutions I've got.
First step I do is state that log 2 ( 1 + 2 x 1 + x ) < 1
Then express the 1 as log 2 2 and so on.
What am I doing wrong?

Answer & Explanation

SoroAlcommai9

SoroAlcommai9

Beginner2022-10-16Added 13 answers

You need to have the followings as well :
log 2 ( 1 + 2 x 1 + x ) > 0         and         1 + 2 x 1 + x > 0 ,
i.e.
1 + 2 x 1 + x > 1.
Hence, the answer will be
x > 1         and         1 + 2 x 1 + x > 1 ,
i.e.
x > 0.

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