Dan's notes, etc
Precalc Formulas
Exponential and Logarithmic Functions (1-5)
Laws of Exponents (1-5) 
- $b^x\cdot b^y = b^{x+y}$
- $\frac{b^x}{b^y} = b^{x\cdot y}$
- $(b^x)^y = b^{x\cdot y}$
- $(a\cdot b)^x = a^x\cdot b^x$
- $\frac{a^x}{b^x} = \left(\frac{a}{b}\right)^x$
Properties of Logarithms (1-5) 
If $a$, $b$, $c>0$, $b\ne1$, and $r$ is any real number, then
\[\begin{array}{lll} \text{1.} & \log_b (a\cdot c) = \log_b (a) + \log_b (c) & \text{(Product Property)} \\ \text{2.} & \log_b\left(\frac{a}{c}\right) = \log_b(a) - \log_b(c) & \text{(Quotient property)} \\ \text{3.} & \log_b(a^r) = r\cdot \log_b(a) & \text{(Power property)} \end{array}\]Change-of-Base Formulas (1-5) 
Let $a>0$, $b>0$, and $a\ne1$, $b\ne1$.
- $a^x = b^{x\cdot \log_b a}$ for any real number $x$.
If $b=e$, this equation reduces to $a^x = e^{x\cdot \log_e a} = e^{x\cdot \ln a}$ - $\log_ax = \frac{\log_b x}{\log_b a}$ for any real number $x>0$.
If $b=e$, this equation reduces to $\log_a x = \frac{\ln x}{\ln a}$.
Hyperbolic Functions (1-5)
Hyperbolic cosine
\(\cosh x = {e^x + e^{-x} \over 2}\)
Hyperbolic sine
\(\sinh x = {e^x - e^{-x} \over 2}\)
Hyperbolic tangent
\(\tanh x = {\sinh x \over \cosh x} = {e^x - e^{-x} \over e^x + e^{-x}}\)