ABC26GN2078 · Logarithms

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

If $a=b^{x}, b=c^{y}$ and $c=a^{z}$, then the value of $x y z$ is equal to
(a)- 1
(b)0
(c)1
(d)abc
Answer
Answer (as printed): C
Explanation
$a=b^{x}, b=c^{y}, c=a^{z} \Rightarrow x=\log _{b} a, y=\log _{c} b, z=\log _{a} c$ $$\begin{aligned} & \Rightarrow \quad x y z=\left(\log _{b} a\right) \times\left(\log _{c} b\right) \times\left(\log _{a} c\right) \\ & \Rightarrow \quad x y z=\left(\frac{\log a}{\log b} \times \frac{\log b}{\log c} \times \frac{\log c}{\log a}\right)=1 . \end{aligned}$$

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

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