Question

If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)² = 20xy 

Answer 1

`log(( x - y)/4) = logsqrt(x) + log sqrt(y)`

∴ `log((x - y)/4) = log(sqrt(x) sqrt(y))`  ...[log m + log n = log mn]

∴ `log((x - y)/4) = logsqrt(xy)`

∴ `(x - y)/4 = sqrt(xy)`

Squaring on both sides, we get

`(x - y)^2/16` = xy

∴ x² – 2xy + y² = 16xy

Adding 4xy on both sides, we get

x² + 2xy + y² = 20xy

∴ (x + y)² = 20xy