Question

PLEASE HELP ME IN THIS QUESTION WITH SOLUTION​

Answer 1

Answer:

1/3

Step-by-step explanation:

Note: For the better understanding,I am replacing x and y with a and b.

We have,

(2.3)ᵃ = (0.23)ᵇ = 1000

Let (2.3)ᵃ = (0.23)ᵇ = 1000 = x.

Apply 'log' on both sides, we get

⇒ log(2.3)ᵃ = log(0.23)ᵇ = log(10)³ = log x

⇒ a log(2.3) = b log(0.23) = 3 log 10 = log x

⇒ a log(2.3) = b log(0.23) = 3 = log x

Now,

(i)

a = logx/log2.3

⇒ (1/a) = log2.3/logx

⇒ (1/a) = log2.3/3

(ii)

b = logb/log0.23

⇒ (1/b) = log0.23/logb

⇒ (1/b) = log0.23/3

(1/a) - (1/b):

⇒ log2.3/3 - log0.23/3

⇒ (1/3)[log2.3 - log0.23]

⇒ (1/3)[log 2.3/log 0.23]

⇒ (1/3)[log 10]

⇒ (1/3) * 1

⇒ 1/3

Hope it helps!