Mathematics for Management -- Supplementary Electronic Materials

Quiz: Exponential & Logarithmic Expressions

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1. Write \( \frac{1}{343} \) as a power of \( 7 \).

\( 7^{1/3} \) \( 7^{-3} \) \( 7^{-49} \) \( 7^3 \)

2. Write \( \sqrt{343} \) as a power of \( 7 \).

\( 7^6 \) \( 7^{7/2} \) \( 7^{2/3} \) \( 7^{3/2} \)

3. Find the solution \( x \) of \( 343 = 49^{x+5} \).

\( x = \frac{7}{2} \) \( x = \frac{338}{7} \) \( x = -\frac{7}{2} \) \( x = 338 \)

4. Simplify the radical expression \( (\sqrt[4]{x^3 y z^5})^{40} \).

\( x^{30} y z^{50} \) \( x^3 y^{10} z^5 \) \( x^{30} y^{10} z^5 \) \( x^{30} y^{10} z^{50} \)

5. Simplify \( \frac{6}{8-\sqrt{5}} \) by rationalizing the denominator.

\( \frac{48 + 6\sqrt{5}}{-3} \) \( \frac{6}{8} - \frac{6}{\sqrt{5}} \) \( \frac{48 + 6\sqrt{5}}{59} \) \( \frac{48 - 6\sqrt{5}}{59} \)

6. Simplify \( \frac{\sqrt{x} - 20}{\sqrt{x} - \sqrt{6}} \) by rationalizing the denominator.

\( \frac{x - 26 \sqrt{x} + 20 \sqrt{6}}{x-6} \) \( \frac{-20 \sqrt{6}}{6} \) \( \frac{x + \sqrt{6x} - 20 \sqrt{x} - 20 \sqrt{6}}{x-6} \) \( \frac{\sqrt{6x} + 20 \sqrt{x} - 20 \sqrt{6}}{6} \)

7. Change \( \log_6(36) = 2 \) to exponential form.

\( 2^6 = 36 \) \( 36^2 = 6 \) \( 6^2 = 36 \) \( 36^6 = 2 \)

8. Write \( \log_b(x/y) \) as two logarithms.

\( \log_b(x) - \log_b(y) \) \( \log_b(x) \cdot \log_b(y) \) \( \log_b(x) + \log_b(y) \) \( \log_b(x) / \log_b(y) \)

9. Write \( \log_3(7) + \log_3(x) - 9 \log_3(y) \) as a single logarithm.

\( \log_3(7x-y^9) \) \( \log_3(\frac{7x}{y^9}) \) \( \log_3(7+x-9y) \) \( \log_3(\frac{x+7}{9y}) \)

10. Find the solution \( x \) of \( \log_6(3x-2) = \log_6(5x-8) \).

\( x = 3 \) \( x = -1 \) \( x = 2 \) no solution

Your grade is: __ of 10

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Solution: 1b; 2d; 3c; 4d; 5d; 6c; 7c; 8a; 9b; 10a

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.