Compute the landmark numbers of a base-7 system. In general, what are the landmark numbers of a base-n system?
Base-7 System Landmark Numbers: 1, 7, 49, 343, 2401, 16807, ...
These are powers of 7: 7⁰ = 1 7¹ = 7 7² = 49 7³ = 343 7⁴ = 2401 7⁵ = 16807
General Rule for Base-n System: The landmark numbers of a base-n system are the powers of n: n⁰ = 1 n¹ = n n² n³ n⁴ ...
Each landmark number is n times the previous one.
Explanation
The chapter states that 'The landmark numbers of a base-n number system are the powers of n starting from n⁰ = 1, n, n², n³, ...' For base-7, this means 7⁰ = 1, 7¹ = 7, 7² = 49, 7³ = 343, 7⁴ = 2401, etc. This pattern holds for any base-n system.
Solution Steps
Identify that landmark numbers in base-7 are powers of 7
List the powers: 7⁰ = 1, 7¹ = 7, 7² = 49, 7³ = 343, 7⁴ = 2401, 7⁵ = 16807, ...
Generalize: For any base-n system, landmark numbers are powers of n
State the pattern: n⁰ = 1, n¹ = n, n², n³, n⁴, ...
Note that each landmark number is n times the previous one