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Q.
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 $(a \neq b \neq c, a, b, c>0)$
Continuity and Differentiability
Solution:
$ \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 $