Question

If $x={\log }_{b}a,y={\log }_{c}b,z={\log }_{a}c$, then $xyz$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B

$1$

Explanation for the correct option:

Find the value of $xyz$ :

Given,

$x={\log }_{b}a,y={\log }_{c}b,z={\log }_{a}c$

We know, ${\log }_{x}y=\frac{\log y}{\log x}$

So,

$\begin{array}{rcl}xyz& =& \frac{\log a}{\log b}\times \frac{\log b}{\log c}\times \frac{\log c}{\log a}\\ & =& 1\end{array}$

Hence, the correct option is B.