Question

The value of $\left({\log }_{b}a\right)\left({\log }_{c}b\right)\left({\log }_{a}c\right)$ is equal to

• A. $0$
• B. $\log abc$
• C. $1$
• D. $10$

Answer 1

The correct option is C $1$

Let $x=\left({\log }_{b}a\right)\left({\log }_{c}b\right)\left({\log }_{a}c\right)$

$\Rightarrow x=\left(\frac{\log a}{\log b}\right)\left(\frac{\log b}{\log c}\right)\left(\frac{\log c}{\log a}\right),[\because {\log }_{y}x=\frac{\log x}{\log y}]\Rightarrow x=1$.