SOLUTION: How many decimal digits are there in the number {{{2005^2005}}}? A. 2005 B. 6621 C. 6620 D. 2004 E. None of these.

We use this principle:

If  is a positive integer which when
written in its scientific notation form is:



that is, where  and  is a non-negative integer,

then  has  decimal digits.

For instance  has
 or  digits. 

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So let's get  in scientific notation:

Let 

Take logs base 10 of both sides:



Use a principle of logs that allows an exponent to be written
as a coefficient:



Use your calculator on the right sidess;



Use the principle of writing a log equation as an 
equivalent exponential equation:



Write the right side as the sum of its whole part plus
its decimal part:



Use the principle 



Use your calculator to find 



Write in standard scientific notation:



Therefore K has 6621 digits, choice B.

Edwin