Question

If `"log" x^2 - "log"sqrt(y)` = 1, express y in terms of x. Hence find y when x = 2.

Answer 1

`"log" x^2 - "log"sqrt(y)` = 1

⇒ `"log"(x^2/sqrt(y))` = log 10

⇒ `x^2/sqrt(y)` = 10

⇒ `sqrt(y) = x^2/(10)`
Squaring both sides, we get

y = `(x^2/10)^2 = x^4/(100)`

Now, when x = 2,
y = `(2^4)/(100) = (16)/(100) = (4)/(25)`.