Number & Units

7 methods · 15 worked questions using these methods

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When an equation involves powers of different but related bases, rewrite every base as a power of their common prime base before combining them. Do not attempt to multiply or divide terms with different bases directly.

Trigger: An equation or expression with indices where the bases are all powers of 2 (like 2, 4, 8) or powers of 3 (like 3, 9, 27, 81).

Instances:
(i) Rewrite each base: $4^{x} = (2^{2})^{x} = 2^{2 x}$ and $2 7^{x} = (3^{3})^{x} = 3^{3 x}$ ;
(ii) Use index laws to combine into a single power on each side;
(iii) Equate the exponents: if $a^{x} = a^{y}$ and $a > 0$ , $a \neq = 1$ , then $x = y$ .

Linked questions for this method (3)

NSAA 2019 Section 1, Part A (Mathematics questions) · Q9

NSAA 2017 Section 1, Part A (Mathematics questions) · Q9

NSAA 2016 Section 1, Part A (Mathematics questions) · Q13