Question

Indices If (8.3) ^x=(0.83)^y = 100 find 1/x - 1/y​

Answer 1

Step-by-step explanation:

(8.3)^x = (0.83)^y = 100 = (10)^2 = k. (let) [ where, k is not equal to zero. ]

So, k^1/x = 8.3 ; k^1/y = 0.83 ; and, k^1/2 = 10

We know, 0.83 × 10 = 8.3

So, k^1/y × k^1/2 = k^1/x

Or, k^(1/y + 1/2) = k^1/x

Or, 1/y + 1/2 = 1/x

Or, 1/x - 1/y = 1/2. (answer)