Logorithmic Functions and their Graphs

  1. Sketch the graph of $y = \log_2 (x+1)$

  2. Evaluate the following:

    1. $\log_2 16$   $\ans{\displaystyle{4}}$

    2. $\log_5 125$   $\ans{\displaystyle{3}}$

    3. $\log 0.001$   $\ans{\displaystyle{-3}}$

    4. $\log_2 \frac{1}{4}$   $\ans{\displaystyle{-2}}$

    5. $\ln 1$   $\ans{\displaystyle{0}}$

    6. $\log 10$   $\ans{\displaystyle{1}}$

    7. $\log_5 5^4$   $\ans{\displaystyle{4}}$

    8. $\log_3 \sqrt[4]{3}$   $\ans{\displaystyle{1/4}}$

    9. $\log 10^{-7}$   $\ans{\displaystyle{-7}}$

    10. $\ln e^{3/4}$   $\ans{\displaystyle{3/4}}$

    11. $\log_4 1$   $\ans{\displaystyle{0}}$

    12. $\ln \sqrt{e}$   $\ans{\displaystyle{1/2}}$

    13. $\log_{64} 4$   $\ans{\displaystyle{1/3}}$

    14. $\log_9 -3$   $\ans{\displaystyle{/textrm{Does not exist}}}$

    15. $\log_9 27$   $\ans{\displaystyle{3/2}}$

    16. $\log_{25} \frac{1}{125}$   $\ans{\displaystyle{-3/2}}$

    17. $\log_{64} \frac{1}{16}$   $\ans{\displaystyle{-2/3}}$

  3. Graph the following. Label intercepts and asymptotes. Give the domain and range.

    1. $\displaystyle{y = \log_2 x}$   $\ians{}$

    2. $\displaystyle{y = \log_2 (x-3)}$   $\ians{}$

    3. $\displaystyle{y = \log_2 \sqrt{x}}$   $\ians{}$

    4. $\displaystyle{y = -1 + \log_2 x}$   $\ians{}$