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].