Elements of Algebra

CHAP. II. OF ALGEBRA. 193 give, $x = \frac{2.7092700}{0.3010300} = \frac{270927}{30103}$, or $x = 9$. Let $5 \times 3^{2x} - 100 = 305$; we add 100, which gives $5 \times 3^{2x} = 405$; dividing by 5, we have $3^{2x} = 81$; and taking the logarithms, $2x \log. 3 = \log. 81$, and dividing by $2 \log. 3$, we have $x = \frac{\log. 81}{2\log. 3}$, or $x = \frac{\log. 81}{\log. 9}$; whence $x = \frac{1.9084850}{0.9542425} = \frac{19084850}{9542425} = 2$. QUESTIONS FOR PRACTICE. 1. If $x - 4 + 6 = 8$, then will $x = 6$. 2. If $4x - 8 = 3x + 20$, then will $x = 28$. 3. If $ax = ab - a$, then will $x = b - 1$. 4. If $2x + 4 = 16$, then will $x = 6$. 5. If $ax + 2ba = 3c^2$, then will $x = \frac{3c^2}{a} - 2b$. 6. If $\frac{x}{2} = 5 + 3$, then will $x = 16$. 7. If $\frac{2x}{3} - 2 = 6 + 4$, then will $2x - 6 = 18$. 8. If $a - \frac{b}{x} = c$, then will $x = \frac{b}{a-c}$. 9. If $5x - 15 = 2x + 6$, then will $x = 7$. 10. If $40 - 6x - 16 = 120 - 14x$, then will $x = 12$. 11. If $\frac{x}{2} - \frac{x}{3} + \frac{x}{4} = 10$, then will $x = 24$. 12. If $\frac{x-3}{2} + \frac{x}{3} = 20 - \frac{x-19}{2}$, then will $x = 23\frac{1}{4}$. 13. If $\sqrt{\frac{2}{3}x} + 5 = 7$, then will $x = 6$. 14. If $x + \sqrt{(a^2 + x^2)} = \frac{2a^2}{\sqrt{(a^2 + x^2)}}$, then will $x=a\sqrt{\frac{1}{3}}$. 15. If $3ax + \frac{a}{2} - 3 = bx - a$, then will $x = \frac{6-3a}{6a-2b}$. 16. If $\sqrt{(12 + x)} = 2 + \sqrt{x}$, then will $x = 4$. 17. If $y + \sqrt{(a^2 + y^2)} = \frac{2a^2}{(a^2+y^2)^{\frac{1}{2}}}$, then will $y=\frac{1}{3}a\sqrt{3}$. 18. If $\frac{y+1}{2} + \frac{y+2}{3} = 16 - \frac{y+3}{4}$, then will $y = 13$. o