TMUA Sed (CoderLovesEggs) Paper 2 with Solutions · Question 14

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Sed (CoderLovesEggs) Paper 2 with Solutions · Q14

Paper 2Powers & logarithmsNumber & counting

An irrational number is a number that cannot be expressed as $\dfrac pq$ , where $p,q$ are integers. $\sqrt2$ and $\log_2 3$ are irrational numbers.

Let $x,y,z$ be nonzero numbers such that the expression

x\log_2(3)+y\log_2(6)+z\log_2(12)

is an integer.

How many values among $x,y,z$ can be irrational?

0,1,2,3

;

0,1,2

;

0,1,3

;

0,2,3

;

1,2,3

;

1,2

;

1,3

;

2,3

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