Question

If $\log \Big(\frac{x-y}{4} \Big) = \log \sqrt{x} + \log \sqrt{y}$, show that (x + y)² = 20xy.

Answer 1

Answer:

Step-by-step explanation:

Hi,  

We will be using the following properties of  

logarithm:

Additive Property : logₐx + logₐy = logₐ(xy) ,

Exponent Property : nlogₐx = logₐxⁿ

and log a = log b, then a = b

Given log (x - y)/4 = log √x + log √y

log √x + log √y = log √x√y

(Using Additve Property), we get

log ( x - y /4) =  log √x√y

So, x - y/4 = √x√y

Squaring on both sides, we get

(x - y)²/ 16 = xy

(x - y)² = 16xy

( x + y)² - 4xy = 16xy

Hence, (x + y)² = 20 xy.

Hope, it helps !