Answer
n$\quad$$\quad$ ⌊lg (n)⌋---2$\quad$$\quad$$\quad$ 1
3$\quad$$\quad$$\quad$ 1
4$\quad$$\quad$$\quad$ 2
5$\quad$$\quad$$\quad$ 2
6$\quad$$\quad$$\quad$ 2
7$\quad$$\quad$$\quad$ 2
8$\quad$$\quad$$\quad$ 3
Work Step by Step
The values in between two integers are scaled down to lowest integer by floor function.
$\left\lfloor \lg 2 \right\rfloor=1$
$\left\lfloor \lg 3 \right\rfloor\approx \left\lfloor 1.59 \right\rfloor\approx 1$
$\left\lfloor \lg 4 \right\rfloor=2$
$\left\lfloor \lg 5 \right\rfloor\approx \left\lfloor 2.32 \right\rfloor\approx 2$
$\left\lfloor \lg 6 \right\rfloor\approx \left\lfloor 2.58 \right\rfloor\approx 2$
$\left\lfloor \lg 7 \right\rfloor\approx \left\lfloor 2.81 \right\rfloor\approx 2$
$\left\lfloor \lg 8 \right\rfloor=3$
