Determining "scale height" for fictitious planet

My first post, I am sure I will have many more! I am so excited to have found this community!

I have a game called Rise: The Vieneo Province and a very old issue that I was hoping to get help with.

According to our wiki for our fictitious planet, the surface pressure is 2631 mb or 2.596 times that of Earth's. However, in the aerodynamic work-up for the aircraft/spacecraft the scale height that is used is 8.0 km or equal to that of Earth's.

I found a formula in which you can solve for the scale-height which requires the known variables of rho (density at a given altitude of z) and surface pressure. I don't know how to reverse engineer from the function of e (is it ln?) or how to determine the density at a given height above the ground.

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Determining "scale height" for fictitious planet

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