Question

If 2^a = 3^b = 6^c then show the relation between a,b and c

Answer 1

heya....


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.


tysm.....$gozmit

Answer 2

2^(a) = 3^(b) = 6^(c)

Let, they all are equal to Z

Z = 2^(a) = 3^(b) = 6^(c)

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Then,

Z = 2^(a)

Z^(1/a) = 2

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Z = 3^b

Z^(1/b) = 3

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Z = 6^(c)

Z^(1/c) = 6

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Z^(1/a) × Z^(1/b) = Z^(1/c)

Z^(1/a + 1/b) = Z^(1/c)

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

(a +b) / ab = c




I hope this will help you

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