Question about natural log function

Question

Does anyone know how to prove that $\ln(x)$ is uniformly continuous on $[1,\infty)$ by just using the definition of a uniformly continuous function?

score 2 · Accepted Answer · answered Feb 20 '14 at 05:02

2

Hint: Show that $|\ln(x)-\ln(y)|\le |x-y|$ for all $x\ge1$ and $y\ge 1$

answered Feb 20 '14 at 05:02

Jose Antonio

score 1 · Answer 2 · edited Apr 13 '17 at 12:21

1

Hint: Use the mean value theorem. See here.

edited Apr 13 '17 at 12:21

Community

answered Feb 20 '14 at 05:16

Mhenni Benghorbal

2 Answers2