Results in a vertical translation (shift up/down) of the graph.

Results in a vertical dilation (stretch or compression) of the graph.

It affects the 'height' of the graph, as all log functions are vertical dilations of each other.

$\log_b(xy) = \log_b(x) + \log_b(y)$

$\log_b(x^n) = n\log_b(x)$

$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$

$\ln(x) = \log_e(x)$

The inverse function to exponentiation. If $b^y = x$, then $\log_b(x) = y$.

The logarithm with base e, denoted as $\ln(x)$.

The mathematical constant e, approximately equal to 2.71828.