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 \geq 0 \text { and }-\log _2 x \geq 0 $
$x \in[\frac{1}{6}, 1$