Question

If x and y are positive real numbers, and log(y) = 3 + 2 log(x), express y in terms of x.

Answer 1

`y=e^(3)*x^(2)`

Explanation:

First, use reduction of power property:

`log(x^(y) )=ylog(x)`

So:

`log(y)=3+log(x^(2) )`

Cancel logarithms by taking exp of both sides:

`e^(log(y)) =e^{3+logx^(2) }`

Keep in mind this:

`x^(y) *x^(z) =x^(y+z)`

Hence:

`y=e^(3) *e^{log(x^(2) )} =e^(3) *x^(2)`