How to get the normalized log-normal distribution equation?

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Seunghyun Moon
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I have a quick(?) question about log-normal distribution. As far as I know, the right-side equation (from wiki) is the PDF of log-normal distribution. However... How I can get the left-side equation...??

I do not know how I can get the normalized log-normal function? please help me...
 
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  • Side-by-side comparison: left, a paper's normalized log-normal size distribution f_LN(x) = 1/((2π)^(1/2) ln σ) exp{-1/2[ln(x/x̄)/ln σ]^2} with x̄ the median; right, the standard log-normal PDF f(x; μ, σ) = 1/(xσ√(2π)) e^(-(ln x - μ)^2/2σ^2).
    log-normal distribution.png
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The RHS equation is the normalized log distribution.
The LHS shows the norm-log distribution... compare with normal distribution.