WAEC 2009 · Paper 2 · Q2

Indices, logarithms & surds

(a)
Solve the simultaneous equations $\log_2 x - \log_2 y = 2$ , $\log_2 (x - 2y) = 3$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Use the quotient law on the first equation: $\log_2 \dfrac{x}{y} = 2$ .
Change to index form: $\dfrac{x}{y} = 2^2 = 4$ , so $x = 4y$ .
Change the second equation to index form: $x - 2y = 2^3 = 8$ .
Substitute $x = 4y$ : $4y - 2y = 8$ , so $y = 4$ .
Then $x = 4 \times 4 = 16$ .
Check: $\log_2 16 - \log_2 4 = 4 - 2 = 2$ ✓ and $\log_2 (16 - 8) = 3$ ✓.
So $x = 16$ and $y = 4$ .

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