How to get numeric value from multiples of 10?

Question

I have the following logic:

1 unit = 1 value

10 units = 2 value

100 units = 3 value

1000 units = 4 value

10000 units = 5 value ... etc

what is the formula where I can plug an arbitrary number of units and it will solve itself for the value and vice versa?

it would be something like X units = Y value

this must be simple but im not great at math, thanks for the help.

Answer 1

Thanks to @dxiv for the answer,

The solution for value is:

value=1+log10(units)

and for units is:

units=10^value−1