Question 4
Let $x$ be a positive real number. Suppose
$$m=\lfloor\log_{10}x\rfloor,\qquad n=\left\lfloor\log_{10}\frac{100}{x}\right\rfloor.$$
Here $\lfloor z\rfloor$ denotes the largest integer less than or equal to $z$. Find the least possible value of $4m^2-3n^2$.
$$m=\lfloor\log_{10}x\rfloor,\qquad n=\left\lfloor\log_{10}\frac{100}{x}\right\rfloor.$$
Here $\lfloor z\rfloor$ denotes the largest integer less than or equal to $z$. Find the least possible value of $4m^2-3n^2$.