# If(log a/b-c)=(log b/c-a)=(log c/a-b) find the value of (a^a) (b^b)(c^c)

Solution:

Let $\\ \log a/b-c=\log b/c-a=\log c/a-b=k$

Then $\log a=k(b-c), \log b=k(c-a); and ; \log c=k(a-b)$

Now, $\\ a\log a+b\log b+c\log c=a\times k(b-c)+b\times k(c-a)+c\times k(a-b)=0\\ \\\therefore \log a^a\times b^b\times c^c=0; or; a^a\times b^b\times c^c=1$

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