**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}*. In the second solution, we match up the indices to*_{b}*xy*.**Review of Important Laws of Indices**

**Solution 1**

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

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