How to find answer of log200 base 2 without calculator? Please help.

Hi We know 2^7 = 128 ; 2^8 =256 so answer will be between 7 and 8 Now check for 2^7.5 which will be 128rt2 which you will get 180 so the answer will be greater than 7.5 , now you can use a bit approximation and approximate it to 7.6 - 7.65

How do we know that answer has to be between 2^7 and 2^8? Kindly help.