Question

Solution set of the equation $\left|1-{\log }_{\frac{1}{6}}x\right|+\left|{\log }_{2}x\right|+2=\left|3-{\log }_{1/6}x-{\log }_{2}x\right|$ is $\left[\frac{a}{b},a\right];a,b\in N$ then the value of $(a+b)$ is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (C)

$|a+b+c|=|a|+|b|+|c|$, then $a,b,c$ has same sign
$1-{\log }_{\frac{1}{6}}x\ge 0\text{ and }-{\log }_{2}x\ge 0$
$x\in [\frac{1}{6},1$