# Logarithmic Expressions

1.  $\rhd$ Introduction to Logarithms (7:01)  Gives the definition of the logarithm after giving several examples such as $2^x = 8$ is equivalent to $\log_2 8 = 3$.  What power do I need to raise $2$ to in order to get $8$? Three.  Several examples, including $\log_x 1 = 0$ for all bases.
2.    $\rhd$  and $\star$ together!  Really it’s an interactive text document covering similar material to the above video, but requiring input from the user.
3.   $\star$ Evaluate a logarithm such as $\log_5 125$.
4.   $\rhd$ Evaluating logarithms (more advanced) (4:20)
Includes $\log_2 8$, $\log_8 2$, $\log_2 \frac{1}{8}$, and $\log_8 \frac{1}{2}.$
5.   $\star$ Evaluate a logarithm (more advanced practice) such as $\log_{\frac{1}{2}} 32$.
6.   $\rhd$ Relationship between exponentials and logarithms (1:42)
Sal rewrites $100= 10^2$ as $\log_{10} 100 = 2$ and $\log_{5}$  $\frac{1}{125}$ = -3 as $5^{-3} = \frac{1}{125}$.
7.   $\rhd$ Relationship between exponentials and logarithms: graphs (4:10)
Deducing equations of exponentials and logarithms from their graphs.
8.   $\rhd$ Relationship between exponentials and logarithms: tables (5:58)
Given incomplete tables of values of $b^x$ and its corresponding inverse function, $\log_b (y)$, Sal uses the inverse relationship of the functions to fill in the missing values.
9.   $\star$ Relationship between exponentials and logarithms.
Students are asked to solve various problems that focus on the relationship between $a^x = b$ and $\log_a(b) = x$