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.
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You missed that. $\displaystyle \ln(y)=\dfrac{\ln(x)+\ln(z)}{2}$
I misread the question as if it said "If y ...". I will probably manage it now.
Use what Plato has stated in his post above to get $\displaystyle y = \sqrt{(xz)}$ and recall the definition of geometric mean.
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
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.
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 $\displaystyle 0.5(ln(xz)) = ln(xz)^{(1/2)} = ln(\sqrt{(xz)})$
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