CAT – Logarithms

Question:
If log2X + log4X = log0.25and x > 0, then x is
A.  6-1/6
B.  61/6
C.  3-1/3
D.  61/3
Correct Answer: (A)
 
Explanation:
log2x + log4x = log0.25
log2x + = log0.25
log2x * = log0.25
log2x * 3 = 2log0.25
log2x3 = log0.256
log2x3 = -log46
log2x3 =
log2x3 =
2log2x3 = -log26
2log2x3 + log26 = 0
log26x6 = 0
6x6 = 1
x6 =
x =  Choice (A).
Level of difficulty 2

Related posts

  • CAT – Linear Quadratic EquationsAugust 8, 2013 CAT – Linear Quadratic Equations Question: 3x + 4|y| = 33. How many integer values of (x, y) are possible? A.  6 B.  3 C.  4 D.  More than 6 Correct Answer: (D) Solution: Let us rearrange the […] Posted in Linear & Quadratic Equations
  • CAT Question – LogarithmsNovember 23, 2012 CAT Question – Logarithms This is a reasonably tough question. But since the messrs conducting CAT seem to have upped the ante on Logarithm, this is probably par for the course Question log5x = a […] Posted in Logarithms
  • CAT Inequalities – Few questionsNovember 19, 2012 CAT Inequalities – Few questions Have given three interesting questions from Inequalities.    Questions  1.  Find the range of x for which (x + 2) (x + 5) > 40. 2.  How many integer values of x […] Posted in Inequalities
  • Inequalities – Interesting QuestionJanuary 28, 2014 Inequalities – Interesting Question Question How many positive integer values can x take that satisfy the inequality (x - 8) (x - 10) (x - 12).......(x - 100) < 0? Answer: 30 Explanation Let us try out […] Posted in Inequalities

3 comments

Leave a Reply

Your email address will not be published. Required fields are marked *