Which is greater e^pi or pi^e?

MHB
Thread starter Poly1
Start date Jan 15, 2013

In summary, e^pi is approximately 23.14, while pi^e is approximately 22.46. This means that e^pi is slightly greater than pi^e. To calculate these values, you can use the formula e^x = 1 + x + (x^2)/2! + (x^3)/3! + ... where x is equal to pi for e^pi and x is equal to e for pi^e. The number e is larger than pi, with e being approximately equal to 2.718 and pi being approximately equal to 3.141. The significance of e^pi and pi^e in mathematics is that they are important mathematical constants used in various branches of math

Jan 15, 2013

Poly1

Which is greater, $e^{\pi}$ or $\pi^{e}$?

I found this when searching for calculus inequalities.

Last edited by a moderator: Jan 16, 2013

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Jan 16, 2013

Fernando Revilla

Gold Member

MHB

Poly said:

I found this when searching for calculus inequalities.

Have a look here:

Math Forum - Ask Dr. Math

Jan 16, 2013

Evgeny.Makarov

Gold Member

MHB

A variation of the same method is to raise both numbers to power $1/(e\pi)$ and find the maximum of $x^{1/x}$.

Related to Which is greater e^pi or pi^e?

1. What is the difference between e^pi and pi^e?

The difference between e^pi and pi^e is that e^pi is approximately 23.14, while pi^e is approximately 22.46. This means that e^pi is slightly greater than pi^e.

2. How do you calculate e^pi and pi^e?

To calculate e^pi, you can use the formula e^x = 1 + x + (x^2)/2! + (x^3)/3! + ... where x is equal to pi. To calculate pi^e, you can use the formula pi^x = 1 + x + (x^2)/2! + (x^3)/3! + ... where x is equal to e. Then simply plug in the values for pi and e and solve the equations.

3. Which number is larger, e or pi?

The number e is larger than pi. It is approximately equal to 2.718, while pi is approximately equal to 3.141. This means that e is approximately 0.423 greater than pi.

4. Why is e^pi greater than pi^e?

This is because the value of e is greater than pi. When raising a number to a power, the larger the base number, the greater the result will be.

5. What is the significance of e^pi and pi^e in mathematics?

Both e^pi and pi^e are important mathematical constants. They are frequently used in calculus, trigonometry, and other branches of mathematics to solve various equations and problems. They also have a special relationship known as the "Euler's identity", which is e^(pi*i) = -1, where i is the imaginary unit.