Question

How do you solve this,step by step :

ln(x)*(2lnx+1)>=0

Answer 1

\(ab\ge 0\) implies they are both positive or both negative.

So let us assume they are both positive.

\(\ln(x)\ge0\) when \(x\ge1\)
and
\(2\ln(x)+1\ge \) implies \(\ln(x)\ge -\frac{1}{2}\) implies \(x\ge \frac{1}{\sqrt{e}}\)\)

Since \(1> \frac{1}{\sqrt{e}}\) we have that the whole thing is non-negative for \(x\ge 1\)

Answer 2

Can you do the same thing for when they are both negative?

Answer 3

Remembering the domain for \(\ln(x) \) is \(x>0\).

Answer 4

Thank you very much :)

Answer 5

np