Question

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Answer 1

2^a = 3^b = 6^c 

so 2 = 6^(c/a) and 3 = 6^(c/b) 

multiply both to get 

6 = 6^( c/ a+ c/b) 

or 1 = c/a + c/b 

or 1 = c(1/a + 1/b) = c(a+b)/(ab) or c = ab/(a+b)

Answer 2

Let 2a=3b=6c=d
So 2a=d
=d1/a=2............(1)
and 3b=d
=d1/b=3............(2)
and also 6c=d
=d1/c=6...............(3)
we know that 6= 2X3
6= 2X3----(4)Now we put the value of 2,3 and6 from equation 1,2 and 3
d1/a X d1/b = d1/c

d(1/a +1/b) = d1/c

so,1/c=1/a+1/b=1/c=(b+a)/ab
Therefore c=ab/a+b