title: SubjectMath.com Practice Test #1, 2017 Edition: A Full Practice Test For the Subject Math Exam
author:  Gilad Pagi 
description: Testimonial by Prof. Karen E Smith (Associate Chair for Graduate Students, Math Department, University of Michigan):<br /><br /><br />The websiteSubjectMath.comoffers a valuable resource for students planning to apply to graduate programs in mathematics and the mathematical sciencesin the United States. TheGREsubject examination in mathematics is required by most departments for admission to graduate programs. The study course provided atSubjectMath.com offers clear, concise online lectures on all the topics tested on the exam in a well-organized series of modules. Students can complete just the modules they most need to review, or, given thatthe fast pace of the exam is often themain difficulty in achieving a high score, students can complete all themodules, where they willlearn many useful tricksfor getting through the problems<b>quickly</b>and accurately.SubjectMath.com also provides a series of practice test booklets that are formatted exactly asthe actual test, allowing students to reproduce exam conditions to maximize the effectiveness of their preparation. In short,SubjectMath.com is an excellent way for students to prepare for theGREtest, reduce stress related to exam taking and maximize their chances of success getting admitted to their dream school.
zlib_text: Created by T. Madas 
   
  Created by T. Madas 
   
   
  LOGARITHMS 
  EXAM 
  QUESTIONS 
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
  
  Created by T. Madas 
   
  Created by T. Madas 
  Question 1   (**) 
  Show clearly that  
  1
  log 36
  log 256
  2log 48
  log 4
  2
  a
  a
  a
  a
  +
  −
  = −
  . 
  proof  
   
   
  Question 2   (**) 
  Simplify 
  2
  2
  log 5
  log 1.6
  +
  , 
  giving the final answer as an integer. 
  3  
   
   
  Question 3   (**+) 
  Given that 
  2p
  x =
   and 
  4q
  y =
  , show clearly that 
  3
  2
  log (
  )
  3
  2
  x y
  p
  q
  =
  +
  . 
   proof  
   
  
  Created by T. Madas 
   
  Created by T. Madas 
  Question 4   (**+) 
  Simplify each of the following expressions, giving the final answer as an integer. 
  a) 
  2
  2
  log 3
  log 24
  −
  . 
  b) 
  2
  1
  log
  4log
  a
  a
  a
  a
  
  
  −
  
  
  
  
  , 
  0
  a >
  , 
  1
  a ≠ . 
  Full workings, justifying every step, must support each answer. 
  3
  −
  , 6  
   
   
  Question 5   (**+) 
  Given that 
  2
  log
  y
  x
  =
  , write each of the following expressions in terms of y . 
  a) 
  2
  2
  log x  
  b) 
  (
  )
  2
  2
  log
  8x
   
  2y , 3
  2y
  +
   
   
   
   
   
   
  
  Created by T. Madas 
   
  Create