Transcendental Numbers...1

What is e^(pi)?

What is pi^(e)?

Can the above be done without a calculator?

 

NO, have to use calculator

 

Ok. Got it.

Check this out:

Infinity...4

 

Do you remember when calculators did not exist? I do!
We used tables of logarithms.
[math]\log(e^{\pi}}= \pi \log(e)= 3.1416(0.4343)= 1.3644[/math].
The you look up 0,3644 in the body of the table to see that 0.3644 is the logarithm of 2.3142. Multiplying that by 10, for the leading "1", [math]e^{\pi}= 23.142[/math].

Similarly, [math]\log(\pi^e}= e \log(\pi)= 2.7183(0.4971)= 1.3514[/math]
Look up 0,3514 in the body of the table to see that 0,3514 is the logarithm of 2.2459. Multiplying that by 10, for the leading "1", [math]\pi^e= 22.459[/math].

 

What is e^pie?
The value of e^pie is approximately 23.1407.

What is pi^e?
The value of pi^e is approximately 22.4592.|

These calculations are typically done using a calculator or computer, as they involve irrational numbers and transcendental functions. While some approximations or logarithmic methods might provide rough estimates, precise values cannot be computed accurately without the aid of a calculator.

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