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

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SUMMARY

The discussion centers on proving the inequality $\pi^e > 5^{1.9}$ without using a calculator. Participants humorously debate the use of a slide rule, with one user jokingly threatening a fine for its use. The conversation emphasizes the importance of analytical reasoning and mathematical proof techniques in establishing the validity of the inequality.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with the mathematical constants $\pi$ and $e$
  • Knowledge of logarithmic comparisons
  • Basic skills in mathematical proof techniques
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  • Research methods for comparing exponential expressions
  • Learn about logarithmic properties and their applications in inequalities
  • Study mathematical proof strategies, particularly for inequalities
  • Explore the significance of constants like $\pi$ and $e$ in mathematical analysis
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Mathematicians, educators, students in advanced mathematics, and anyone interested in analytical proof techniques and the properties of exponential functions.

anemone
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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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