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