Answer key

1. (a). $-2, -3$

   (b). $4, 0$

2. (a). $2+2\sqrt{10}$, $2-2\sqrt{10}$

   (b). $2, -14$

3. (a). $4+\sqrt{15}$, $4+\sqrt{15}$

   (b). $-3+\sqrt{14}$, $-3-\sqrt{14}$

4. (a).$0.32$, $-1.57$

   (b). $3.85$, $0.65$

5. (a).

   

   (b).

   

6. (a).

   

   (b).

   

7. (a). $169$ feet

   (b). $\$9711$

   (c). $200$

8. (a).

   

   (b).

   

9. (a). $(-\infty, -2)\cup (1, 5)$

   (b). $(-\infty, -5)\cup[3, \infty)$

10. (a). $3x+4$; $5x-8$ and, $-28$

    (b). $2x^3-10x^2$; $2x^2+x-5$ and, $-15$

11. (a). (i) $-\dfrac{2}{35}$; (ii) $-6, 6$.

    (b). (i) $0$; (ii) $-2$.

12. (a). $16$ and $6$

    (b). $48$ and $35$

13. (a). $\dfrac{8x}{9x-7}$; $\left(-\infty, \dfrac{7}{9}\right )\cup \left(\dfrac{7}{9}, \infty\right)$ and, $\left(-\infty, \dfrac{8}{9}\right )\cup \left(\dfrac{8}{9}, \infty\right)$

    (b). $\dfrac{-x-7}{6x-1}$; $\left(-\infty, \dfrac{1}{6}\right )\cup \left(\dfrac{1}{6}, \infty\right)$ and, $\left(-\infty, -\dfrac{1}{6}\right )\cup \left(-\dfrac{1}{6}, \infty\right)$

14. (a). $\log_3 81=4$

    (b). $8^2=64$

15. (a).

    

    (b).

    

16. (a). $\log y+3 \log z +5 \log(y+3)-2\log x$

    (b). $\dfrac{1}{2}\log y-\dfrac{9}{2}\log(z+2)-2\log x$

17. (a). $\log_m \left(\dfrac{w^{\frac{1}{3}} x^2}{y}\right )$

    (b). $\log_a \left ( \dfrac{y^2z^2}{w^6}\right)$

18. (a). $0.921$

    (b). $-0.732$

19. (a). $-\dfrac{3}{4}$

    (b). $34$

20. (a). $12$

    (b). $79$

    (c). No solution

21. (a). $\dfrac{3}{2}$

    (b). $-5$

22. (a). $\dfrac{8\log 9}{\log 9 -7\log 13}$

    (b). $\dfrac{-9\log 7}{\log 7 +10\log 2}$

23. (a). $4$ years.

    (b). $13$ years.