IntegerLength

IntegerLength[n] gives the number of digits in the base 10 representation of n.

IntegerLength[n, b] gives the number of digits in base b.

Examples

Decimal digits:

IntegerLength[12345]
(* 5 *)

Binary digits:

IntegerLength[255, 2]
(* 8 *)

Please visit the official Wolfram Language Reference for more details.