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Difference between revisions of "1983 AIME Problems/Problem 1"
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== Problem ==
 
== Problem ==
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Let <math>x</math>,<math>y</math>, and <math>z</math> all exceed <math>1</math>, and let <math>w</math> be a positive number such that <math>\log_xw=24</math>, <math>\log_yw=40</math>, and <math>\log_{xyz}w=12</math>. Find <math>\log_zw</math>.
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Let <math>x</math>,<math>y</math>, and <math>z</math> all exceed <math>1</math>, and let <math>w</math> be a positive number such that <math>\log_xw=24</math>, <math>\displaystyle \log_y w = 40</math>, and <math>\log_{xyz}w=12</math>. Find <math>\log_zw</math>.
  
 
== Solution ==
 
== Solution ==

Revision as of 23:43, 23 July 2006

Problem

Let $x$,$y$, and $z$ all exceed $1$, and let $w$ be a positive number such that $\log_xw=24$, $\displaystyle \log_y w = 40$, and $\log_{xyz}w=12$. Find $\log_zw$.

Solution

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