## anonymous one year ago WILL AWARD MEDAL How do you solve the inequality (x^2)(e^x) ln x > 0?? @nincompoop @Nnesha @zepdrix @jagr2713

1. zzr0ck3r

well $$e^x>0$$ for all $$x$$, $$x^2>0$$ for all $$x\ne 0$$ and $$\ln(x)>0$$ for all $$x>1$$. So ?

2. zzr0ck3r

hint: the $$ln(x)$$ factor trumps them all.

3. anonymous

sorry i don't really understand where this is going.

4. anonymous

@zzr0ck3r

5. anonymous

These are things we can do without affecting the direction of the inequality: Add (or subtract) a number from both sides. Multiply (or divide) both sides by a positive number. Simplify a side. Hoped this helped :)

6. zzr0ck3r

What I am saying is that $$x^2e^x\ln(x)>0 \iff \ln(x)>0\iff x>1$$