There are a series of questions from JackDamery which relate to what you want - it's probably worth reading through these to get the jist of what worked for him. The problem is not the VCO of course but the log convertor.

At one point I suggested using a lower power dc-to-dc convertor to produce split rails so maybe this can be considered. Other than that it boils down to using digital methods i.e. reading a pot voltage into an ADC, converting to digital, applying a log function digitally and reproducing an analogue voltage output that is the log of the input voltage.

There are a series of questions from JackDamery which relate to what you want - it's probably worth reading through these to get the jist of what worked for him. The problem is not the VCO of course but the log convertor.

At one point I suggested using a lower power dc-to-dc convertor to produce split rails so maybe this can be considered. Other than that it boils down to using digital methods i.e. reading a pot voltage into an ADC, converting to digital, applying a log function digitally and reproducing an analogue voltage output that is the log of the input voltage.