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Let n (arak-1 ·*a1a0)3 be the base 3 expansion of a positive integer n. Find the base 3 expansion of the positive integer n9".

Let n (arak-1 ·*a1a0)3 be the base 3 expansion of a positive integer n. Find the base 3 expansion of the positive integer n9".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Let \( n = (a_k a_{k-1} \cdots a_1 a_0)_3 \) be the base 3 expansion of a positive integer \( n \). Find the base 3 expansion of the positive integer \( n 9^n \). **Explanation:** This mathematical problem involves understanding the representation of numbers in base 3. The notation \( (a_k a_{k-1} \cdots a_1 a_0)_3 \) indicates that the integer \( n \) is expressed in base 3, where each \( a_i \) (where \( i \) ranges from 0 to \( k \)) represents a digit in the base 3 system. The challenge is to determine the base 3 representation of the product of \( n \) and \( 9^n \). There are no graphs or diagrams accompanying this problem. It involves purely algebraic manipulations and conversions.
Transcribed Image Text:**Problem Statement:** Let \( n = (a_k a_{k-1} \cdots a_1 a_0)_3 \) be the base 3 expansion of a positive integer \( n \). Find the base 3 expansion of the positive integer \( n 9^n \). **Explanation:** This mathematical problem involves understanding the representation of numbers in base 3. The notation \( (a_k a_{k-1} \cdots a_1 a_0)_3 \) indicates that the integer \( n \) is expressed in base 3, where each \( a_i \) (where \( i \) ranges from 0 to \( k \)) represents a digit in the base 3 system. The challenge is to determine the base 3 representation of the product of \( n \) and \( 9^n \). There are no graphs or diagrams accompanying this problem. It involves purely algebraic manipulations and conversions.
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