Question

2^a=3^b=6^c
Show that 1/c =1/b+1/a.

Answer 1

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.

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