[H2_ACJC2000P1Q15b] Adders use Logs to Multiply

Question

Introduction

     Here is a question on arithmetic progressions, and not the first question of its type.  As you know, the schools in Singapore mimic questions from the GCE ‘A’ Levels, as well as from one another.  Before we go into the solution, let us go through some things you need to know.

Prerequisites

Solution

Remarks

     You might observe that the argument of the logarithm,  pq^n–1,  forms a geometric progression.  Indeed, any logarithm of a geometric progression will form an arithmetic progression.  However, this is not something that you should memorise.  Just stick to the basic principles and work it out.  Mathematics is not about memorisation.  It is about observing and understanding links between things.  If you want to memorise, ask: Why do adders like to live among logs?  Answer: That’s the way they multiply.  J

Heuristics Used

H04. Look for pattern(s)

H09. Restate the problem in another way

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* GCE ‘A’ Levels, H2 Mathematics 

* International Baccalaureate Mathematics 

* other syllabuses that involve logarithms, arithmetic and geometric progressions