How to properly solve this inequality 2^x < 3/4

vegetatzz8s

vegetatzz8s

Answered question

2022-11-23

How to properly solve this inequality 2 x < 3 4 ?
How to properly solve this inequality?
2 x < 3 4
I know that it will be something like that:
x ? log 2 3 4
But I don't know how to decide if it should be > or <.

Answer & Explanation

bocescGXN

bocescGXN

Beginner2022-11-24Added 8 answers

You have
2 x < 3 4
equivalently
ln 2 x < ln 3 4
x ln 2 < ln 3 4
x < ln 3 4 ln 2
x < log 2 3 4
Observe that log 2 ( ) is strictly increasing on x > 0:
( log 2 ) ( x ) = 1 ln 2 1 x > 0 , x > 0.

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