Date: May 19, 2013 2:20 PM
Subject: Floor of the log equation: s = (floor(log10(x))+1)*x - round((10^(floor(log10(x))+1)-10)/9)

Hi guys! I need your help to solve this equation:

I need to find 'x' for a given 's'. Both of them are natural numbers (>0).

I don't know how to handle the floor term.

[octave/matlab format]
s = (floor(log10(x))+1)*x - round((10^(floor(log10(x))+1)-10)/9);

[or TeX}
s = \left( \lfloor\log(x)\rfloor+1 \right)x - \frac{10^{\lfloor\log(x)\rfloor+1}-10}{9}

[or image]

Exact or approximate values are good.

Is there a solution? How do I solve it?

Are there any methods to search & find a solution?