## anonymous one year ago How do you solve this,step by step : ln(x)*(2lnx+1)>=0

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1. zzr0ck3r

$$ab\ge 0$$ 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 $$x\ge 1$$

2. zzr0ck3r

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

3. zzr0ck3r

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

4. anonymous

Thank you very much :)

5. zzr0ck3r

np