Question

If log (x + y) = log x + log y, then y is equal to ______.

विकल्प

• `x/(x - 1)`

• `(x + 1)/x`

• `(x - 1)/x`

• `x/(x + 1)`

Answer 1

If log (x + y) = log x + log y, then y is equal to `underlinebb(x/(x - 1))`.

Explanation:

Use the product rule

log x + log y = log (xy)

So log (x + y) = log (xy) 

⇒ x + y = xy (logs defined) 

Rearranging gives y(x – 1) = x. 

Hence `y = x/(x - 1)`.