Question

Let u=ln x and v= ln y. Write ln( √x · y^2) in terms of u and v.

Answer 1

c

Explanation:

Answer 2

C

Explanation:

We can use 2 properties of logarithms to write this:

1. ln(x*y) = lnx + ln y

2. ln(a^b) = b ln a

Using property 1, we can write as:

`ln(√(x) *y^(2))\\=ln(√(x) )+ln(y^2)\\=ln(x^{(1)/(2)})+2lny\\=(1)/(2)lnx+2lny`

We know u = lnx and v = ln y, we simply substitute it now:

`(1)/(2)lnx+2lny\\=(1)/(2)u+2v`

the correct answer is C