3. The zeros of the polynomial $p(x)=x^{3}-13 x^{2}+39 x-27$ are the first three terms of an increasing geometric sequence.

(a) Write the first five terms and the general term of the sequence.

(b) Which term of the given geometric sequence is the solution to the equation $\log (15-3 x)-\log x=\log (x-1) ?$
3. Roots $x_{1}=1, x_{2}=3, x_{3}=9$ each for 0.5 points
(a) Sequence: 1, 3, 9, 27, 81 (only in this order) ..... 0.5 points
$a_{n}=3^{n-1}$ ..... 1 point
(b) $\log \frac{15-3 x}{x}=\log (x-1)$ ..... 0.5 points
$\frac{15-3 x}{x}=x-1$ ..... 0.5 points
$x^{2}+2 x-15=0$ ..... 0.5 points
Solution: $x_{1}=-5$ ..... 0.5 points
$x_{2}=3$ ..... 0.5 points
Answer: The solution to the equation is the second term of the sequence. ..... 0.5 points