Method of Moments: Lognormal Distribution

From Lognormal Distribution, we know that 

Thus

and so

from which it follows that

and so

or

Since

it follows that

and so

which gives us the estimates for μ and σ based on the method of moments.

Reference

Genos, B. F. (2009) Parameter estimation for the Lognormal distribution
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2927&context=etd