please show the steps for derive the log normal distribution

1.2.1 The Log Normal Distribution Equation(3) - Recall Normal (Gaussian) Distribution : 1.2.1 The Log Normal Distribution Equation(4) y=s2e(2/2u2=s21exp[2s2(uu)2]. y=2lnsx1exp[2ln2sf(lnxlnxf)2]=2lnSf1exp[2ln2sfln2(x/xf)] where xR=exp[N1i=1Nlnxi] Geometric mean - Log Normal Distribution : The Log of the quantity is governed by a normal sf=exp[i=1NN1ln2(xi/xr)]1/2 Geometric standard deviation distribution. If we make the substitution: ulnx,x is our Homework 1: Derive the above equation observable now 9/3/2022 Derive the Log normal distribution equation based on the normal distribution equation