A number N has n digits where n = floor(log_10(N))+1 (floor the greatest integer less than or equal to its argument)

8^41* 5^116 = [10^(log_10(8))]^41 * [10^(log_10(5))]^116

.................. = 10^(41*log_10(8)+log_10(5)*116) ~= 10^(118.107)

so floor(log_10(8^41* 5^116))+1 = 119, so 8^41* 5^116 has 119 digits.

RonL