Question

2. If 2^a = 3^b = 6^c, then the value of c is​

Answer 1

Answer:

The answer is the 4th option

Step-by-step explanation:

Let 2^a=3^b=6^c=n

2^a=n this can be written as 2=(n)^(1/a)

Similarly 3=(n)^(1/b)

6=(n)^(1/c)

2 × 3 = 6

(n)^(1/a) × (n)^(1/b) = (n)^(1/c)

Here the bases are same i.e the base is n

so we use the formula n^a × n^b = n^(a+b)

So n^(1/a) × n^(1/b) = n^((1/a + 1/b ))

= n^((a+b)/ab)

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

Here the bases are same i.e the base is n

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

c = ab/(a+b)

The answer is ab/a+b