College Algebra, 4th Edition

Practice Test B

1. Solve the equation $3^{-x}=9.$

   1. {2}

   2. $\{-2\}$

   3. $\left\{{\displaystyle \frac{1}{2}}\right\}$

   4. $\left\{-{\displaystyle \frac{1}{2}}\right\}$

   5. {ln 2}

2. Solve the equation ${\log }_{5}x=2.$

   1. {10}

   2. {25}

   3. $\left\{{\displaystyle \frac{5}{2}}\right\}$

   4. $\left\{{\displaystyle \frac{2}{5}}\right\}$

   5. {2}

3. State the range and asymptote of $y=e^{-x}-1.$

   1. $(0,\infty );y=-1$

   2. $(-1,\infty );y=-1$

   3. $(-\infty ,\infty );y=-1$

   4. $(-1,\infty );y=1$

   5. $(\infty ,1);y=1$

4. Evaluate ${\log }_{4}64.$

   1. 16

   2. 8

   3. 2

   4. 3

   5. 4

5. Find the solution of the exponential equation ${\left({\displaystyle \frac{1}{3}}\right)}^{1-x}=3.$

   1. $\left\{-{\displaystyle \frac{1}{3}}\right\}$

   2. $\left\{{\displaystyle \frac{1}{3}}\right\}$

   3. {1}

   4. {2}

6. Evaluate log 0.01.

   1. $-1.99999999$

   2. $-2$

   3. 2

   4. 100

7. Which of the following expressions is equivalent to $\ln 7+2\ln x?$

   1. $\ln (7+2x)$

   2. $\ln (7x^2)$

   3. ln (9x)

   4. ln (14x)

8. Solve the equation $2^{x^2}=3^x.$

   1. {0}

   2. $\left\{{\displaystyle \frac{\ln 3}{\ln 2}}\right\}$

   3. $\left\{0,{\displaystyle \frac{\ln 3}{\ln 2}}\right\}$

   4. $\{0,\ln 3-\ln 2\}$

9. Solve the equation $e^{2x}-e^x-6=0.$

   1. $\{-\ln 2\}$

   2. $\{-\ln 3\}$

   3. {ln 6}

   4. {ln 3}

10. Rewrite the expression $\ln {\displaystyle \frac{3x^2}{{(x+1)}^{10}}}$ in expanded logarithmic form.

    1. $\ln 6x-10\ln x+1$

    2. $2\ln 3x-10\ln (x+1)$

    3. $2$