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\begin{document}


Review of Logarithms\qquad \qquad \qquad \qquad \qquad \qquad \qquad
Name\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

\vspace{1pt}

\vspace{1pt}Condense the following.

\qquad Example. \ $\log _{3}x+\log _{3}4=\log _{3}4x$

\vspace{1pt}

\vspace{1pt}1. \ $\log _{4}2x+\log _{4}3\qquad \qquad \qquad \qquad \qquad $%
2. \ $\log _{5}x-\log _{5}3\qquad \qquad \qquad \qquad $3. \ $\log 10+\log
6-\log x$

\vspace{1pt}

\vspace{1pt}

\vspace{1pt}Expand the following.

\vspace{1pt}\qquad Example. \ $\log _{5}60=\log _{5}6+\log _{5}10$

\vspace{1pt}

4. \ $\log _{3}6x\qquad \qquad \qquad \qquad \qquad \qquad \qquad 5.\log 
\dfrac{x}{4}\qquad \qquad \qquad \qquad \qquad \qquad $6. \ $\log _{3}\left( 
\dfrac{3x}{2}\right) $

\vspace{1pt}

\vspace{1pt}

Remember: \ $\log 10=1\qquad \qquad \log _{3}3=1\qquad \qquad \qquad \log
_{x}x=1\qquad \qquad \qquad \log _{6}6=1$

\vspace{1pt}

\vspace{1pt}

Solve the following.

\qquad Example. \ \ $\log _{3}x+\log _{3}4=\log _{3}16-\log _{3}x\qquad
\qquad $Condense the logs.

\vspace{1pt}

\qquad \qquad \qquad \qquad $\log _{3}4x=\log _{3}\dfrac{16}{x}\qquad $Since
the bases match we can drop the logarithms.

\vspace{1pt}

\vspace{1pt}\qquad \qquad \qquad \qquad $4x=\dfrac{16}{x}\qquad \qquad $Solve

\vspace{1pt}

\qquad \qquad \qquad \qquad $4x^{2}=16\qquad \qquad $

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^{2}=4$

\qquad \qquad \qquad \qquad $x=\pm 2\qquad \qquad -2$ is extraneous.

\vspace{1pt}

7. \ $\log _{5}(x+1)-\log _{5}3=\log _{5}3+\log _{5}x\qquad \qquad $8. \ $%
2\log x=\log (x+12)$ \ (Hint: \ $3\log x=\log x^{3})$

\vspace{1pt}

\vspace{1pt}

Solve.

\vspace{1pt}

9. \ $\log _{3}(x+4)=4\qquad \qquad \qquad $10. \ log$_{5}\dfrac{1}{25}%
=x\qquad \qquad \qquad $11. \ $\log _{x}64=3$

\vspace{1pt}

\vspace{1pt}

\vspace{1pt}

\vspace{1pt}

\vspace{1pt}

Given the following information, approximate the following logarithms.

\vspace{1pt}

\qquad \qquad $\log 5=0.699\qquad \qquad \log 15=1.176$

\vspace{1pt}

12. \ $\log 3\qquad \qquad \qquad \qquad $13. \ $\log 25\qquad \qquad \qquad 
$14. \ $\log \dfrac{1}{3}$

\vspace{1pt}

\vspace{1pt}

\vspace{1pt}

\vspace{1pt}

\qquad \qquad \qquad \qquad

\vspace{1pt}

\qquad \qquad \qquad \qquad \qquad

\end{document}
