Question

Find the value of n, where n is an integer and 2n-5 x 6 2n-4= 1/12^4×2​

Answer 1

Answer:

Value of n is 0.

Step-by-step explanation:

Given problem is 2^(n-5) × 6^(2n-4) = 1/ 12^4 ×2

                             2^(n-5) × 6^(2n-4) = (12^4 × 2)^-1

                             (∵  1/ 12^4 ×2 = (12^4 × 2)^-1)

⇒ 2^(n-5) × 6^(2n-4) = [(6×2)^4 × 2]^-1

⇒2^(n-5) × 6^(2n-4) = (2^4 × 2 × 6^4)^-1

According to law of indices:

a^ m × b^ m =( ab)^m

⇒2^(n-5) × 6^(2n-4) = (2^5 ×6^4)^-1

⇒2^(n-5) × 6^(2n-4) = 2^-5 × 6^-4

Now comparing on both sides we have

2^n-5 = 2^-5      and    6^(2n-4) =  6^-4

n-5 = -5                             2n-4 = -4

n = -5+5                            2n = -4+4

∴n = 0                                 2n=0

                                           ∴ n=0