binomial

for any number x, no. of digits in x = [log x] +1 ...[] denotes greatest integer function
therefore,
log 5³⁰ = 30 log 5 =30(log10 - log2) =30(1-0.3010)=30(0.699)=20.97

hence no. of digits= [20.97]+1 = 21

it is just basic logic, like suppose we have a 2 digit no. say n,
then 10≤n<100
taking log on all sides ,

1≤log n <2

hence for any n such that ,
10^m < n < 10^m+1
then we can say n has m+1 digits

now taking log,

m < log n <m+1
hence [log n] = m
now

no. of digits = m+1 = [log n] +1