Контрольные задания > Решите уравнение: 39.8. a) $3^x = 9$; в) $3^x = 27$; б) $3^x = \frac{1}{3}$; г) $3^x = \frac{1}{81}$. 39.9. a) $5^x = \sqrt{5}$; в) $8^x = \sqrt[3]{8}$; б) $(\frac{1}{3})^x = 81$; г) $(\frac{4}{5})^x = \frac{16}{25}$. 039.10. a) $2^{8x} = 128$; в) $3^{2x} = \frac{1}{27}$; б) $6^{8x} = 216$; г) $(\frac{1}{7})^{5x} = \frac{1}{343}$.
Вопрос:

Решите уравнение: 39.8. a) $$3^x = 9$$; в) $$3^x = 27$$; б) $$3^x = \frac{1}{3}$$; г) $$3^x = \frac{1}{81}$$. 39.9. a) $$5^x = \sqrt{5}$$; в) $$8^x = \sqrt[3]{8}$$; б) $$(\frac{1}{3})^x = 81$$; г) $$(\frac{4}{5})^x = \frac{16}{25}$$. 039.10. a) $$2^{8x} = 128$$; в) $$3^{2x} = \frac{1}{27}$$; б) $$6^{8x} = 216$$; г) $$(\frac{1}{7})^{5x} = \frac{1}{343}$$.

Ответ:

39.8.
  1. a) $$3^x = 9$$
    $$3^x = 3^2$$
    $$x = 2$$
  2. b) $$3^x = \frac{1}{3}$$
    $$3^x = 3^{-1}$$
    $$x = -1$$
  3. c) $$3^x = 27$$
    $$3^x = 3^3$$
    $$x = 3$$
  4. d) $$3^x = \frac{1}{81}$$
    $$3^x = 3^{-4}$$
    $$x = -4$$
39.9.
  1. a) $$5^x = \sqrt{5}$$
    $$5^x = 5^{\frac{1}{2}}$$
    $$x = \frac{1}{2}$$
  2. b) $$8^x = \sqrt[3]{8}$$
    $$8^x = 2$$
    $$(2^3)^x = 2^1$$
    $$2^{3x} = 2^1$$
    $$3x = 1$$
    $$x = \frac{1}{3}$$
  3. c) $$(\frac{1}{3})^x = 81$$
    $$(3^{-1})^x = 3^4$$
    $$3^{-x} = 3^4$$
    $$-x = 4$$
    $$x = -4$$
  4. d) $$(\frac{4}{5})^x = \frac{16}{25}$$
    $$(\frac{4}{5})^x = (\frac{4}{5})^2$$
    $$x = 2$$
039.10.
  1. a) $$2^{8x} = 128$$
    $$2^{8x} = 2^7$$
    $$8x = 7$$
    $$x = \frac{7}{8}$$
  2. b) $$3^{2x} = \frac{1}{27}$$
    $$3^{2x} = 3^{-3}$$
    $$2x = -3$$
    $$x = -\frac{3}{2}$$
  3. c) $$6^{8x} = 216$$
    $$6^{8x} = 6^3$$
    $$8x = 3$$
    $$x = \frac{3}{8}$$
  4. d) $$(\frac{1}{7})^{5x} = \frac{1}{343}$$
    $$(\frac{1}{7})^{5x} = (\frac{1}{7})^3$$
    $$5x = 3$$
    $$x = \frac{3}{5}$$
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