Let H(n) be the number of healphy people at the day n  (those who are still healphy);

let I(n) be the number of ill people of the day n 
    (the cumulative sum of ill, formerly ill and death persons to the day n).


For the Day-0 we have, from the condition

    H(0) = 2621 - 71 = 2550;

    I(0) = 71


And in following days we have

    H(n) = (1-0.12)*H(n-1) = 0.88H(n-1),

    I(n) = 2621 - H(n),

in accordance with the problem's description.


Notice that these formulas and this setup are not the same as in the post by the other tutor:


    +------------------------------------------------------------------+
    |    everyday decreasing the number of healthy people by 12%,      |
    |        as described in the problem, is NOT THE SAME as           |                                                                   
    |      everyday increasing the number of ill people by 12%.        |
    +------------------------------------------------------------------+


Next, to solve the problem using formulas, notice that 95% of the population be infected means
that 5% of 2621 is still healthy, or  0.05*2621 = 131 is healthy  (rounded).


So, we are looking to find n such that  H(n) =   is still greater than 131:

     >= 131.


To solve this inequality, divide both sides by 2550

     >=   = 0.05137;


take the logarithm base 10 of both sides

    n*log(0.88) >= log(0.05137)


express and calculate "n"

    n >=  = 23.22321...


For the final answer, you should round this decimal number to the closest lesser integer, which is 23.