Question

(3/5)^n=0.216 find the Value of n

Answer 1

The value of n is 3.

Step-by-step explanation:

We are given,

(3/5)ⁿ=0.216

The above-given question can be solved by two methods:

Method 1:

(3/5)ⁿ=0.216

⇒ [3/5]ⁿ = [0.6]³

⇒ [0.6]ⁿ = [0.6]³

⇒ n = 3

Method 2:

(3/5)ⁿ=0.216

Taking log on both sides

⇒ log [3/5]ⁿ = log 0.216

⇒ n log [3/5] = log 0.216 …… [∵ log aᵇ = b log a]

⇒ n log [0.6] = log 0.216

⇒ n [- 0.221] = [- 0.665]

⇒ n = 0.665/0.221

⇒ n = 3