Question

The value of $a^{\log \left(b/c\right)}\times b^{\log \left(c/a\right)}\times c^{\log \left(a/b\right)}$ is

• A. 0
• B. 1
• C. -1
• D. None of these

Answer 1

The correct option is B 1

We know that $a^{\log b}=b^{\log a}$ and $\log \left(a/b\right)=\log a-\log b$.

Now, using above properties:

$=a^{\log \left(b/c\right)}\times b^{\log \left(c/a\right)}\times c^{\log \left(a/b\right)}=$ $a^{\log \left(b\right)-\log c}\times b^{\log \left(c\right)-\log a}\times c^{\log \left(a\right)-\log b}$

$=\frac{a^{\log b}}{a^{\log c}}\times \frac{b^{\log c}}{b^{\log a}}\times \frac{c^{\log a}}{c^{\log b}}=1$................[ because $x^{\log y}=y^{\log x}$]