WAEC 2008 · Paper 2 · Q4

(a)
Solve the equation $2\log x - \log(1 - x) = \log(2 - x)$ .
(b)
If Ade gives ₦5 out of what he has to Chidi, the two of them will have equal amounts. If Chidi gives ₦5 to Ade, Ade will have twice as much as Chidi. How much did each of them have initially?
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Use the power law: $2\log x = \log x^2$ .
Use the division law on the left: $\log x^2 - \log(1 - x) = \log\frac{x^2}{1 - x}$ .
The logs are equal, so the numbers are equal: $\frac{x^2}{1 - x} = 2 - x$ .
Multiply out: $x^2 = (2 - x)(1 - x) = 2 - 3x + x^2$ .
The $x^2$ terms cancel: $3x = 2$ , so $x = \frac23$ (and $1 - x$ , $2 - x$ are positive, so the logs exist).