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2020 AMC 12A Problems/Problem 10

Revision as of 10:27, 1 February 2020 by Quacker88 (talk | contribs) (→‎Solution)

Solution

Any logarithm in the form $\log_{a^b} c = \frac{1}{b} \log_a c$.

so \[\log_2{(\log_{2^4}{n})} = \log_{2^2}{(\log_{2^2}{n})}.\]

becomes

\[\log_2{\frac{1}{4}(\log_{2}{n})} = \frac{1}{2}\log_2{\frac{1}{2}(\log_2{n})}.\]

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