Question 47806
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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.



<pre>
Take decimal logarithm of {{{3^500}}}.

    {{{log((3^500))}}} = 500*log(3) = 500*0.477121255 = 238.5606274.


It tells us that  {{{3^500)}}}  is  {{{10^238}}}  multiplied by  {{{10^0.5606274}}}

    {{{3^500}}} = {{{10^238*10^0.5606274}}} = {{{3.636*10^238}}},  approximately.


<U>ANSWER</U>.  {{{3^500}}} is approximately {{{3.636*10^238}}}.
</pre>

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.