TLDR: The LM391x are all the same chip except for the resistors in the reference divider chain. LM3914 has a linear divider chain, LM3915 had a 3dB/step logarithmic divider chain, and LM3916 had a logarithmic divider chain optimized for VU meters.
As all except LM3914 are discontinued, if you *MUST* use a LM391x dot/bar chip, and need a logarithmic response, and cant find an affordable and trustworthy N.O.S. supplier for LM3915 or '3916, you'll need to put a logarithmic converter (e.g. an OPAMP with a diode in its feedback loop) in front of a LM3914.