Question

If $\frac{\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b}$, then the value of $\left(a^a{b}^b{c}^c\right)$ is $(a\ne b\ne c,a,b,c>0)$

• A. $abc$
• B. $\frac{1}{abc}$
• C. 1
• D. $\log (abc)$

Answer 1

Answer: (C)

$\log \left(a^a\cdot b^b\cdot c^c\right)=a\log a+b\log b+c\log c=a(b-c)k+b(c-a)k+c(a-b)k=0$
$\Rightarrow \left(a^a{b}^b{c}^c\right)=1$