$\log_a(m^{-1}) = -\log_am$
$\log_a1 = 0$ and $\log_aa = 1$
+
## Inverse functions
Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$
$k$ is a constant
For continuous growth, $k > 0$
For continuous decay, $k < 0$
+
+## Graphing expomnential functions
+
+$$f(x)=Aa^{k(x-b)} + c, \quad \vert a > 1$$
+
+- **$y$-intercept** at $(0, {{1+c} \over {a^b}})$
+- **horizontal asymptote** at $y=c$
+- **domain** is $\mathbb{R}$
+- **range** is $(c, \infty)$
+- dilation of factor $A$ from $x$-axis
+- dilation of factor $1 \over k$ from $y$-axis
+
+## Graphing logarithmic functions
+
+$log_e x$ is the inverse of $e^x$ (reflection across $y=x$)
+
+$$f(x)=A \log_a k(x-b) + c$$
+
+where
+- **domain** is $(b, \infty)$
+- **range** is $\mathbb{R}^+$
+- **vertical asymptote** at $x=b$
+- $y$-intercept exists if $b<0$
+- dilation of factor $A$ from $x$-axis (reflection across $x$-axis when $A < 0$)
+- dilation of factor $1 \over k$ from $y$-axis (reflection across $y$-axis when $k < 0$)
+