# Math Help - arithmetic mean and geometric mean

1. ## arithmetic mean and geometric mean

If LNy is the arithmetic mean of LNx and LNz show that y is the geometric mean of x and z.

I found that xz=LN(xz) hence xz=1=y.

2. You missed that.
$\ln(y)=\dfrac{\ln(x)+\ln(z)}{2}$

3. I misread the question as if it said "If y ...". I will probably manage it now.

4. Use what Plato has stated in his post above to get $y = \sqrt{(xz)}$ and recall the definition of geometric mean.

5. LNy=0.5(LNx+LNz)
If x,y and z are in G.P. then (xz)^2=y.
LN(xz)^2=0.5(LNx+LNz)
=0.5(LN(xz))
=LN(xz)^2

6. Originally Posted by Stuck Man
LNy=0.5(LNx+LNz)
If x,y and z are in G.P. then (xz)^2=y.
LN(xz)^2=0.5(LNx+LNz)
=0.5(LN(xz))
=LN(xz)^2
You've got squares where you should have square roots.

7. Originally Posted by Stuck Man
LNy=0.5(LNx+LNz)
If x,y and z are in G.P. then (xz)^2=y.
LN(xz)^2=0.5(LNx+LNz)
=0.5(LN(xz))
=LN(xz)^2
$0.5(ln(xz)) = ln(xz)^{(1/2)} = ln(\sqrt{(xz)})$