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Lets say i have a dataset that follows a double log normal distribution.

these 2 functions intersect at $(x,y)$ when

$y = p(\frac{1}{\sigma_1\sqrt{2\pi}}exp(-\frac{(x-\mu_1)^2}{2\sigma_1^2})) = (1-p)(\frac{1}{\sigma_2\sqrt{2\pi}}exp(-\frac{(x-\mu_2)^2}{2\sigma_2^2}) )$

how do i back transform $x$ after getting it?

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