Not sure if you actually meant logarithmic or exponential. An exponential tax rate would mean that the more you own the next unit of value would be a lot more in tax, while a logarithmic tax rate would mean that the more you own the next unit of value would be a lot less in tax. See x2 versus log2(x) (or any logarithm base, really). The exponential (x2) would start slow and then increase fast, and the logarithmic one would start increasing fast and then go into increasing slowly.
Logarithmic scale of increasing property tax rate
Not sure if you actually meant logarithmic or exponential. An exponential tax rate would mean that the more you own the next unit of value would be a lot more in tax, while a logarithmic tax rate would mean that the more you own the next unit of value would be a lot less in tax. See x2 versus log2(x) (or any logarithm base, really). The exponential (x2) would start slow and then increase fast, and the logarithmic one would start increasing fast and then go into increasing slowly.
https://www.desmos.com/calculator/7l1turktmc