Question

Answer the following:

If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x² + y² = 27xy

Answer 1

`log ((x - y)/5) = 1/2 logx + 1/2 log y`

Multiplying throughout by 2, we get

`2log ((x - y)/5)` = log x + log y

∴ `log((x - y)/5)^2` = log xy

∴ `(x - y)^2/25` = xy

∴ x² – 2xy + y² = 25xy

∴ x² + y² = 27xy