MHB Prove $\pi^e > 5^{1.9}$ Without Calculator

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Prove, without the use of a calculator, $\pi^e>5^{1.9}$.
 
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Can I use my slide rule? (If I can find it. It's packed away.)

-Dan
 
Dan, if you use it in your solution, then I will have to report you to the authority and you will be fined $250. Hehehe...
 

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