Question Number 10040 by FilupSmith last updated on 21/Jan/17

Show that ⌊log_(10) (x)+1⌋ give the number of digits for x∈Z

Answered by mrW1 last updated on 21/Jan/17

let x be an integer with n digits, then 10^(n−1) ≤x<10^n log_(10) 10^(n−1) ≤log_(10) (x)<log_(10) 10^n n−1≤log_(10) (x)<n n≤log_(10) (x)+1<n+1 ⇒⌊log_(10) (x)+1⌋=n