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1962 AHSME Problems/Problem 17

Revision as of 10:31, 17 April 2014 by Hukilau17 (talk | contribs)

Problem

If $a = \log_8 225$ and $b = \log_2 15$, then $a$, in terms of $b$, is:

$\textbf{(A)}\ \frac{b}{2}\qquad\textbf{(B)}\ \frac{2b}{3}\qquad\textbf{(C)}\ b\qquad\textbf{(D)}\ \frac{3b}{2}\qquad\textbf{(E)}\ 2b$

Solution

Using the change-of-base rule: $a = \frac{\log 225}{\log 8}$ and $b = \frac{\log 15}{\log 2}$. \[\frac{a}b = \frac{\log 225 \log 2}{\log 8 \log 15}\] 

\[a = b \dot \frac{\log 225 \log 15} \dot \frac{\log 2 \log 8}\] (Error compiling LaTeX. Unknown error_msg)

\[a = b \log_{15} 225 \log_8 2\] \[a = \boxed{\frac{2b}3 \textbf{ (B)}}\]

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