Prove (ln(x))/(x) <= log_(10) 2

Brylee Shepard

Brylee Shepard

Answered question

2022-08-08

Prove ln ( x ) x log 10 2
How would I go about proving the following inequality?
ln ( x ) x log 10 2
Is there an algebraic solution and if not, why?

Answer & Explanation

Jaydan Gilbert

Jaydan Gilbert

Beginner2022-08-09Added 16 answers

log 10 2 = ln 2 ln 10 . Then, for all positive x,
x 2 x ln 10
Then you apply ln to both sides (given that it's monotonically increasing), and you have the inequality you want.

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