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Difference between revisions of "1981 AHSME Problems/Problem 15"

(Created page with "==Problem== If <math>b>1</math>, <math>x>0</math>, and <math>(2x)^{\log_b 2}-(3x)^{\log_b 3}=0</math>, then <math>x</math> is <math>\textbf{(A)}\ \dfrac{1}{216}\qquad\textbf...")
 
(→‎Problem)
 
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<math>\textbf{(A)}\ \dfrac{1}{216}\qquad\textbf{(B)}\ \dfrac{1}{6}\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ \text{not uniquely determined}</math>
 
<math>\textbf{(A)}\ \dfrac{1}{216}\qquad\textbf{(B)}\ \dfrac{1}{6}\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ \text{not uniquely determined}</math>
 +
 +
==Solution==
 +
<math>\boxed {B}</math>

Latest revision as of 19:09, 23 October 2021

Problem

If $b>1$, $x>0$, and $(2x)^{\log_b 2}-(3x)^{\log_b 3}=0$, then $x$ is

$\textbf{(A)}\ \dfrac{1}{216}\qquad\textbf{(B)}\ \dfrac{1}{6}\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ \text{not uniquely determined}$

Solution

$\boxed {B}$

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