Question

If 2^a = 3^b = 6^c, then show that
c = (ab)/(a+b)

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

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

So c = ab / a+b

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