SOLUTION: What is the approximate value of {{{ 3^sqrt(999) }}}?

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Question 1192841: What is the approximate value of ?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
That's not too big to just punch into a scientific or graphing
calculator.  You get the answer immediately as
1.203242085 x 1015

That's no fun.

Your teacher should have given you one that will overflow any
calculator's capacity.  Like putting a couple more 9's under
that square root to make it too big for calculators:



You can't punch that on a calculator.  It'll overflow.
So you'll have to use logarithms.  Set x equal to the quantity



Use your calculator to get the exponent 



Take the log (base 10) of both sides:





Use your calculator to get the right side:



Raise 10 to both sides' power:



The left side is just x.  The right side is too big for 
calculators, so split the exponent into an integer and
a decimal



Write the right side as the product of powers of 10



Next use your calculator to get 





That's the answer in scientific notation to the problem
I made up.  But that's the way to do them if they're too
big for a calculator.

Edwin

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