Difference between revisions of "1962 AHSME Problems/Problem 17"

Revision as of 21:17, 3 October 2014

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

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

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)

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

1962 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40
All AHSME Problems and Solutions

@@ Line 10: / Line 10: @@
 <cmath>a = b \log_{15} 225 \log_8 2</cmath>
 <cmath>a = \boxed{\frac{2b}3 \textbf{ (B)}}</cmath>
+==See Also==
+{{AHSME 40p box|year=1962|before=Problem 16|num-a=18}}
+[[Category:Introductory Algebra Problems]]
+{{MAA Notice}}