Question

If 2^a = 3 ^b = 6 ^C, then find the relation between a,b and c.

Answer 1

Answer:

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)