Difference between revisions of "2020 AMC 12A Problems/Problem 10"
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| − | <cmath>\log_2{\frac{1}{4} | + | <cmath>\log_2{\frac{1}{4}\log_{2}{n}} = \frac{1}{2}\log_2({\frac{1}{2}\log_2{n}}).</cmath> |
Revision as of 11:28, 1 February 2020
Solution
Any logarithm in the form 
.
so ![\[\log_2{(\log_{2^4}{n})} = \log_{2^2}{(\log_{2^2}{n})}.\]](http://latex.artofproblemsolving.com/d/7/2/d72fc0c7356556c8b9a92b56f1491527f1ae442a.png)
becomes
![\[\log_2{\frac{1}{4}\log_{2}{n}} = \frac{1}{2}\log_2({\frac{1}{2}\log_2{n}}).\]](http://latex.artofproblemsolving.com/1/5/f/15fae9d14b80f3d06e4253de1dbe13f7120f2c97.png)
