Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.
- $\rhd$ Intro to logarithm properties (1 of 2) (9:15) Examples illustrating the properties $\log_BA+\log_BC=\log_B(AC)$ and $\log_BA-\log_BC=\log_B\left(\dfrac{A}{C}\right).$
- $\rhd$ Intro to logarithm properties (2 of 2) (10:04) Examples illustrating the properties $A\cdot\log_BC=\log_B\left(C^A\right)$ and $\log_BA=\dfrac{\log_CA}{\log_CB}$ (change of base formula). This video also shows how to find $\log_2 \left(\sqrt{\dfrac{32}{\sqrt 8}}\right).$
- $\rhd$ Expand logarithmic expression (3:56) Expand $\ln\left(\sqrt{x^3\cdot \sqrt[4]{y}}\right)$
- * Practice Type of problem: (scroll down)
- Find $\log_2(3a)$.
- Condense $\log_5(2y)+\log_5(8)$.
- Expand $\log_b\left(\dfrac{4}{c}\right)$.
- Condense $\log(3z)-\log(8)$.
- Expand $\log_7(x^5)$.
- Condense $6\ln y$.
- + challenge problems
- $\rhd$ Using the properties of logarithms: multiple steps (2:09) Simplify $\log_5\dfrac{25^x}{y}$.
