[S2_20151122IXBQ] A Bonus for your Index Fun?

Question

Introduction

     This is a “bonus” question which most likely came from an Integrated Programme (IP) school.  It really tests the wits of students’ knowledge of indices and problem solving tactics.  I present two solutions without the use of logarithms.  The first solution uses reciprocal indices and the matching of the base ^a/_b.  In the second solution, we match up the indices to  xy.

Review of Important Laws of Indices

Solution 1

 

Solution 2

Remarks

     No logs from any forest were harmed in the process of making this blog post.  J

Heuristics Used

H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in another way

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* challenge for Lower Secondary Mathematics (Secondary 2)

* GCE ‘O’ Level “Elementary” Mathematics (revision)

* other syllabuses that involve algebra and indices