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Let 2^a=3^b=6^c =k
2 = k^(1/a), 3 = k^(1/b) and 6= k^(1/c)
2*3=6
k^(1/a)*k^(1/b) = k^(1/c)
k^(1/a +a/b)= k^(1/c)
1/a +a/b = 1/c
a+b/ab = 1/c
c= ab/a+b Hence, Proved.
2 = k^(1/a), 3 = k^(1/b) and 6= k^(1/c)
2*3=6
k^(1/a)*k^(1/b) = k^(1/c)
k^(1/a +a/b)= k^(1/c)
1/a +a/b = 1/c
a+b/ab = 1/c
c= ab/a+b Hence, Proved.
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