How to solve e^x problems efficiently?

[furyhecla]

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How do you solve math problems with 'e' efficiently and quickly?

For instance: e^-3/2.... what is the answer?

A practice solution I have simply writes e^-3/2 = 0.22... but how do you do this without a calculator or long-han

This is what I did, but it takes a long time:

e^-3/2
=(2.7^1/2)*(2.7^-4/2)
=(2.7^1/2)*(2.7^-2)
=1.64/2.7^2
=1.64/7.29
=.22

Any other way to 'intuitively' solve these? I'm looking for ways to speed up my math solving... thanks.

 

[Rabolisk]

e^-3/2 = 1/e^3/2
e^3/2 is in between e^1 and e^2 or 2.7 and ~7 or 8. Somewhere between 4 and 5 seem like the right answer, which yields somewhere between 0.2 and 0.25. If you only had one answer choice between 0.15 and 0.3, that is good enough for me.

 

[Etorphine]

hint. 2.303*logX=lnx