CAT - Logarithms

Question:
If log₂X + log₄X = log_0.25and 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:

log₂x + log₄x = log_0.25

log₂x + = log_0.25

log₂x * = log_0.25

log₂x * 3 = 2log_0.25

log₂x³ = log_0.256

log₂x³ = -log₄6

log₂x³ =

log₂x³ =

2log₂x³ = -log₂6

2log₂x³ + log₂6 = 0

log₂6x⁶ = 0

6x⁶ = 1

x⁶ =

x =  Choice (A).

Level of difficulty 2