Very simple math problem~

2^3 = 8
2^4 = 16
2^n = 10

Then, n = log2(10) = 3.321928094887362. Not an integer.

Based on your question "Three-digit binary represents octal, four-digit binary represents hexadecimal", it can be deduced that you should mean
The minimum of three-digit binary is 000 and the maximum is 111. Its range is exactly 0-7, which constitutes octal. One digit, so One octal requires three binary digits
And the minimum
four digit binary is 000, the maximum is 1111, its range is exactly 0-15, which constitutes one hexadecimal digit, so One hexadecimal The system requires four binary digits
And
according to the above, there should be no such statement about how many binary digits correspond to one decimal digit. The decimal notation method based on 10 as the base is 0,1,2,3,4,5,6, 7,8,9
while binary
000->0
001->1
010->2
011->3
100->4
101->5
110->6
111->7
1000->8

How many binary digits correspond to one decimal digit? It spans three and four digits
So by inferring, you can know why three binary digits represent octal and four binary digits represent hexadecimal