SOLUTION: How do I solve- If 2^a=3^b=6^c, show that c=ab/a+b. Thank you

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Question 979068: How do I solve-
If 2^a=3^b=6^c, show that c=ab/a+b.
Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
2^a=6^c ---> (2^a)^(b/a+b)=(6^c)^(b/a+b) ---> 2^(ab/(a+b))=6^(cb/(a+b))
3^b=6^c ---> (3^b)^(a/a+b)=(6^c)^(a/a+b) ---> 3^(ab/(a+b))=6^(ca/(a+b))
Then, multiplying
[ 2^(ab/(a+b)) ] [ 3^(ab/(a+b)) ] = [ 6^(cb/(a+b)) ] [ 6^(ca/(a+b)) ]
(2*3)^(ab/(a+b)) = 6^[ cb/(a+b) + ca/(a+b) ]
6^(ab/(a+b)) = 6^[(cb+ca)/(a+b)]
6^(ab/(a+b)) = 6^[c(b+a)/(a+b)]
6^(ab/(a+b)) = 6^c ------> ab/(a+b) = c