# 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

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

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