Given ln 2=x and ln5=y, use the properties of logarithms to write ln square root 20 in terms of x and y.

ln (sqrt20) = ln
[(20)^(1/2)]

We'll use the power property of
logarithms:

ln [(20)^(1/2)] = (ln
20)/2

ln 20 = ln (4*5)

We'll
use the product property of logarithms:

ln(a*b) = ln a + ln
b

ln (4*5) = ln 4 + ln 5

But
ln 4 = ln (2^2)

ln 4 = 2*ln
2

ln 20 = 2*ln 2 + ln 5

ln 20
= 2x + y

ln (sqrt20) =
(2x+y)/2

The given logarithm written in terms
of x and y is: ln (sqrt20) = (2x+y)/2.