Question 35646
Did you just want to calculate this?  If so just type it into a calculator "log", "log", 200:
{{{log(10,(log(10,200))) }}} = 0.3619 approximately.


If you care to try to understand the concept of like "log (log 200)", it means that you are taking the log of a log.   To start out with an easier one and to try to put it in perspective, try 

{{{log(10,(log(10,1000))) }}}.


You already know {{{log(10, 1000) }}} means "what power" would you have to raise 10 to in order to get 1000?  The answer is clearly 3, right?  So, {{{log(10,1000) }}} = 3.


Then {{{log(10,(log(10,1000))) }}} means {{{log(10,3) }}}, which by calculator would be about 0.477.


See my Lesson Plans about Logarithms on algebra.com, or on my own website under "Math in Living Color" and then "College Algebra".


R^2 at SCC