ABC26GN2076 · Logarithms

Subject: General Aptitude · Chapter: Logarithms · Exam: · Marks: · Difficulty:

The value of $\left[\frac{1}{\log _{(p / q)} x}+\frac{1}{\log _{(q / r)} x}+\frac{1}{\log _{(r / p)} x}\right]$ is
(a)0
(b)1
(c)2
(d)3
Answer
Answer (as printed): A
Explanation
Given expression $$\begin{aligned} & =\log _{x}\left(\frac{p}{q}\right)+\log _{x}\left(\frac{q}{r}\right)+\log _{x}\left(\frac{r}{p}\right) \\ & =\log _{x}\left(\frac{p}{q} \times \frac{q}{r} \times \frac{r}{p}\right)=\log _{x} 1=0 . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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