Answer:
C
Step-by-step 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:
[tex]ln(\sqrt{x} *y^{2})\\=ln(\sqrt{x} )+ln(y^2)\\=ln(x^{\frac{1}{2}})+2lny\\=\frac{1}{2}lnx+2lny[/tex]
We know u = lnx and v = ln y, we simply substitute it now:
[tex]\frac{1}{2}lnx+2lny\\=\frac{1}{2}u+2v[/tex]
the correct answer is C
