Simplify the following expression

Question

5lnx - 1/2 lny + 3 lnz

Answer 1

Since
ln(a)+ln(b) = ln(ab)
ln(a)-ln(b) = ln(a/b)
(1/2)ln(a) = ln(sqrt(a), and
3ln(a) = ln(a³)

5 ln(x) = ln(x⁵)
-(1/2)ln(y) = ln(1/sqrt(y))
3 ln(z) = ln(z³)

So
5lnx - 1/2 lny + 3 lnz
=ln(x⁵ * 1/sqrt(y) * ... )

Can you now complete the answer and simplify?

Answer 2

Mathmate - Yes, I can thank you!