How does multiplying the input of a log function by a constant affect its graph?
Results in a vertical translation (shift up/down) of the graph.
How does raising the input of a log function to a power affect its graph?
Results in a vertical dilation (stretch or compression) of the graph.
How does changing the base of a logarithmic function affect its graph?
It affects the 'height' of the graph, as all log functions are vertical dilations of each other.
What is the product property of logarithms?
$\log_b(xy) = \log_b(x) + \log_b(y)$
What is the power property of logarithms?
$\log_b(x^n) = n\log_b(x)$
What is the change of base formula for logarithms?
$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$
How to express natural log in base e?
$\ln(x) = \log_e(x)$
What is a logarithm?
The inverse function to exponentiation. If $b^y = x$, then $\log_b(x) = y$.
What is the natural logarithm?
The logarithm with base *e*, denoted as $\ln(x)$.
What is the base of the natural logarithm?
The mathematical constant *e*, approximately equal to 2.71828.
