If 2^a = 3^b = 6^c then show that .

• Given: 2^a = 3^b = 6^c

• To prove:

Now,

Let 2^a = 3^b = 6^c = k (where k is any constant)…(1)

From equation 1, we get

2^a = k ⇒ 2 =

∴ …(2)

3^b = k ⇒ 3 =

∴ …(3)

6^c = k ⇒ 6 =

∴ …(4)

Multiplying equation 2 and 3 we get

(∵ a^maⁿ = a^{m + n})

But, From(4)

Substituting 6 = in the above equation, we get

⇒

∴

Hence Proved.