# CAT Practice : Exponents and Logarithms

Logarithm with non-integer bases are slightly trickier. Have a go at this one!

## Logarithm - Inequalities

Q.1: If log2X + log4X = log0.25$\sqrt {6}$ and x > 0, then x is
1. 6-1/6
2. 61/6
3. 3-1/3
4. 61/3

• Correct Answer
Choice A. 6-1/6

## Detailed Solution

log2x + log4x = log0.25$\sqrt {6}$

log2x + ${log_{2}x \over log_{2}4}$ = log0.25$\sqrt {6}$

log2x * ${3 \over 2}$ = log0.25$\sqrt {6}$

log2x * 3 = 2log0.25$\sqrt {6}$

log2x3 = log0.256

log2x3 = -log46

log2x3 = ${-log_2{6} \over log_2{4}}$

log2x3 = ${-log_2{6} \over 6}$

2log2x3 = -log26

2log2x3 + log26 = 0

log26X6 = 0

6x6 = 1

x6 = ${1 \over 6}$

x = $\sqrt[6]{1 \over 6}$

Answer Choice (A)

Correct Answer: 6-1/6

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Exponents and Logarithms

With every extra hour you log in for this topic, it becomes exponentially simpler.