**Question:**
If log_{2}X + log_{4}X = log_{0.25}and x > 0, then x is
A. 6^{-1/6}

B. 6^{1/6}

C. 3^{-1/3}

D. 6^{1/3}

**Correct Answer: (A)**

** **

**Explanation:**

log_{2}x + log_{4}x = log_{0.25}
log_{2}x + = log_{0.25}
log_{2}x * = log_{0.25}
log_{2}x * 3 = 2log_{0.25}
log_{2}x^{3} = log_{0.25}6

log_{2}x^{3} = -log_{4}6

log_{2}x^{3} =
log_{2}x^{3} =
2log_{2}x^{3} = -log_{2}6

2log_{2}x^{3} + log_{2}6 = 0

log_{2}6x^{6} = 0

6x^{6} = 1

x^{6} =
x = Choice (A).
**Level of difficulty 2**

### Related posts

- August 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
- November 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
- November 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
- January 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

good one

Yup good one

Yup really