Difference between revisions of "2020 AMC 12A Problems/Problem 10"
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Any logarithm in the form <math>\log_{a^b} c = \frac{1}{b} \log_a c</math>. | Any logarithm in the form <math>\log_{a^b} c = \frac{1}{b} \log_a c</math>. | ||
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| + | so <cmath>\log_2{(\log_{2^4}{n})} = \log_{2^2}{(\log_{2^2}{n})}.</cmath> | ||
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| + | becomes | ||
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| + | <cmath>\log_2{\frac{1}{4}(\log_{2}{n})} = \frac{1}{2}\log_2{\frac{1}{2}(\log_2{n})}.</cmath> | ||
Revision as of 10:27, 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/0/3/9/039495e03806c291b722929722e8f5c43fe78d57.png)
