Difference between revisions of "2019 AMC 12A Problems/Problem 12"

(Created page with "==Problem== Positive real numbers <math>x \neq 1</math> and <math>y \neq 1</math> satisfy <math>\log_2{x} = \log_y{16}</math> and <math>xy = 64</math>. What is <math>(\log_2{...")
 
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==Solution==
 
==Solution==
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We know that <math>\log_2(x) = \log_y(16)</math>
  
 
==See Also==
 
==See Also==

Revision as of 18:11, 9 February 2019

Problem

Positive real numbers $x \neq 1$ and $y \neq 1$ satisfy $\log_2{x} = \log_y{16}$ and $xy = 64$. What is $(\log_2{\tfrac{x}{y}})^2$?

$\textbf{(A) } \frac{25}{2} \qquad\textbf{(B) } 20 \qquad\textbf{(C) } \frac{45}{2} \qquad\textbf{(D) } 25 \qquad\textbf{(E) } 32$

Solution

We know that $\log_2(x) = \log_y(16)$

See Also

2019 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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
All AMC 12 Problems and Solutions

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