SOLUTION: what is 3^500?

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Question 47806: what is 3^500?
Found 3 solutions by consc198, ikleyn, greenestamps:
Answer by consc198(59) About Me  (Show Source):
You can put this solution on YOUR website!
=3^500
No simplification!!

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
.
what is 3^500?
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        In his post, @consc198 responds "no simplification!".
        But the problem does not ask to simplify. It asks to evaluate (or to estimate) the value.
        @consc198 is so ignorant of mathematics that does not understand the meaning of the request.

        Meanwhile, the solution is standard and straightforward. 


Take decimal logarithm of 3%5E500.

    log%28%283%5E500%29%29 = 500*log(3) = 500*0.477121255 = 238.5606274.


It tells us that  3%5E500%29  is  10%5E238  multiplied by  10%5E0.5606274

    3%5E500 = 10%5E238%2A10%5E0.5606274 = 3.636%2A10%5E238,  approximately.


ANSWER.  3%5E500 is approximately 3.636%2A10%5E238.

Solved.

This is so important skill that every educated person
should have it in his or her hands, as well as in his or her mind.



Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


You can find exact values of large integers like this using the PARI online calculator. Go to

pari.math.u-bordeaux.fr

How to find the calculator when you get to that web site apparently depends on your browser.

ANSWER: 3^500 =

36360291795869936842385267079543319118023385026001623040346035832580600191583895484198508262979388783308179702534403855752855931517013066142992430916562025780021771247847643450125342836565813209972590371590152578728008385990139795377610001